Many processes in nature and technology can only be described by partial differential equations, e.g., heating or cooling processes, the propagation of acoustic or electromagnetic waves, or fluid mechanics. Additionally to challenges in modeling, in various applications the manipulation or controlling of the modeled system is also of interest in order to obtain a certain purpose. One ends up in optimal control problems, i.e. nonlinear optimization problems governed by partial differential equations. By means of the control the solution of the partial differential equation (the “state”) is influenced, where a certain cost functional has to be minimized simultaneously. However, in many technical applications additional pointwise constraints to the state or the control are essential, for instance in steel hardening or in optimization of semiconductor crystal growth.

Particularly, the treatment of state-constrained optimal control problems governed by partial differential equations is of high interest since Lagrange multipliers with respect to the state constraints are in general only measures. Thus, the development and investigation of efficient discretization strategies and optimization algorithms is exceedingly challenging. Thereby, the combination of aspects of nonlinear optimization and numerics of partial differential equations is crucial. The analysis of the underlying partial differential equation regarding solvability and regularity is another important task. Primarily, this knowledge allows the correct formulation of state constraints or a priori error estimates for discretization strategies.

The solution of nonlinear optimization problems poses new mathematical challenges if the underlying data are nondifferentiable or random. This situation is in particular encountered in problems with equilibrium constraints (MPECs) or in stochastic optimization, both of them being important for modeling technological or economic processes. Equilibria in power markets or the stochastic unit commitment problem in power production may serve as examples here. In such cases, classical results concerning structure, stability, and numerics do no longer apply and have to be worked out afresh.
Distortion compensation of a roller bearing by optimal control of an interface between materials with different densities (cf. WIAS Preprint 1792).


Publications

  Monographs

  • M. Hintermüller, M. Hinze, Ch. Kahle, T. Keil, Chapter 13: Fully Adaptive and Integrated Numerical Methods for the Simulation and Control of Variable Density Multiphase Flows Governed by Diffuse Interface Models, in: Transport Processes at Fluidic Interfaces, D. Bothe, A. Reusken, eds., Advances in Mathematical Fluid Mechanics, Birkhäuser, Springer International Publishing AG, Cham, Switzerland, 2017, pp. 305--353, (Chapter Published), DOI 10.1007/978-3-319-56602-3 .

  • M. Hintermüller, D. Wegner, Distributed and Boundary Control Problems for the Semidiscrete Cahn--Hilliard/Navier--Stokes System with Nonsmooth Ginzburg--Landau Energies, in: Topological Optimization and Optimal Transport in the Applied Sciences, M. Bergounioux, E. Oudet, M. Rumpf, G. Carlier, Th. Champion, F. Santambrogio, eds., 17 of Radon Series on Computational and Applied Mathematics, De Gruyter, Berlin, 2017, pp. 40--63, (Chapter Published).

  • P. Colli, A. Favini, E. Rocca, G. Schimperna, J. Sprekels, eds., Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs: In Honour of Prof. Gianni Gilardi, 22 of Springer INdAM Series, Springer International Publishing, 2017, pp. xii--571, (Collection Published).
    Abstract
    This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.

  • D. Hömberg, G. Hu, eds., Issue on the workshop ``Electromagnetics -- Modelling, Simulation, Control and Industrial Applications'', 8, no. 3 of Discrete Contin. Dyn. Syst. Ser. S, American Institute of Mathematical Sciences, Springfield, 2015, 259 pages, (Collection Published).

  • P. Colli, G. Gilardi, D. Hömberg, E. Rocca, eds., Special Issue dedicated to Jürgen Sprekels on the Occasion of his 65th Birthday, 35, no. 6 of Discrete Contin. Dyn. Syst. Ser. A, American Institute of Mathematical Sciences, Springfield, 2015, 472 pages, (Collection Published).

  • P. Deuflhard, M. Grötschel, D. Hömberg, U. Horst, J. Kramer, V. Mehrmann, K. Polthier, F. Schmidt, Ch. Schütte, M. Skutella, J. Sprekels, eds., MATHEON -- Mathematics for Key Technologies, 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, 453 pages, (Collection Published).

  • A. Mielke, Chapter 21: Dissipative Quantum Mechanics Using GENERIC, in: Recent Trends in Dynamical Systems -- Proceedings of a Conference in Honor of Jürgen Scheurle, A. Johann, H.-P. Kruse, F. Rupp, S. Schmitz, eds., 35 of Springer Proceedings in Mathematics & Statistics, Springer, Basel et al., 2013, pp. 555--585, (Chapter Published).
    Abstract
    Pure quantum mechanics can be formulated as a Hamiltonian system in terms of the density matrix. Dissipative effects are modeled via coupling to a macroscopic system, where the coupling operators act via commutators. Following Öttinger (2010) we use the GENERIC framework (General Equations for Non-Equilibrium Reversible Irreversible Coupling) to construct thermodynamically consistent evolution equations as a sum of a Hamiltonian and a gradient-flow contribution, which satisfy a particular non-interaction condition. One of our models couples a quantum system to a finite number of heat baths each of which is described by a time-dependent temperature. The dissipation mechanism is modeled via the canonical correlation operator, which is the inverse of the Kubo-Mori metric for density matrices and which is strongly linked to the von Neumann entropy for quantum systems. Thus, one recovers the dissipative double-bracket operators of the Lindblad equations but encounters a correction term for the consistent coupling to the dissipative dynamics. For the finite-dimensional and isothermal case we provide a general existence result and discuss sufficient conditions that guarantee that all solutions converge to the unique thermal equilibrium state. Finally, we compare of our gradient flow formulation for quantum systems with the Wasserstein gradient flow formulation for the Fokker-Planck equation and the entropy gradient flow formulation for reversible Markov chains.

  • D. Hömberg, F. Tröltzsch, eds., System Modeling and Optimization, 25th IFIP TC 7 Conference, CSMO 2011, Berlin, Germany, September 12--16, 2011, 391 of IFIP Advances in Information and Communication Technology, Springer, Heidelberg [et al.], 2013, 568 pages, (Collection Published).

  • K. Kunisch, G. Leugering, J. Sprekels, F. Tröltzsch, eds., Optimal Control of Coupled Systems of Partial Differential Equations, 158 of Internat. Series Numer. Math., Birkhäuser, Basel et al., 2009, 345 pages, (Collection Published).

  • B. Denkena, D. Hömberg, E. Uhlmann, Mathematik für Werkzeugmaschinen und Fabrikautomatisierung, in: Produktionsfaktor Mathematik. Wie Mathematik Technik und Wirtschaft bewegt, M. Grötschel, K. Lucas, V. Mehrmann, eds., acatech diskutiert, acatech, Springer, Berlin, Heidelberg, 2008, pp. 279--299, (Chapter Published).

  • R. Henrion, A. Kruger, J. Outrata, eds., Special Issue on: Variational Analysis and Generalised Differentiation, 16 of Set-Valued Analysis, Springer, Heidelberg, 2008, xii+231 pages, (Collection Published).

  • K. Kunisch, G. Leugering, J. Sprekels, F. Tröltzsch, eds., Control of Coupled Partial Differential Equations, 155 of Internat. Series Numer. Math., Birkhäuser, Berlin, 2007, 382 pages, (Collection Published).

  • P. Neittaanmäki, D. Tiba, J. Sprekels, Optimization of Elliptic Systems: Theory and Applications, Springer Monographs in Mathematics, Springer, New York, 2006, xvi+514 pages, (Monograph Published).

  • K.-H. Hoffmann, I. Lasiecka, G. Leugering, J. Sprekels, F. Tröltzsch, eds., Optimal Control of Complex Structures, 139 of International Series of Numerical Mathematics, Birkhäuser, Basel Boston Berlin, 2002, 289 pages, (Monograph Published).

  Articles in Refereed Journals

  • M. Eigel, R. Müller, A posteriori error control for stationary coupled bulk-surface equations, IMA Journal of Numerical Analysis, (2017), published online on 9.3.2017, DOI 10.1093/imanum/drw080 .
    Abstract
    We consider a system of two coupled elliptic equations, one defined on a bulk domain and the other one on the boundary surface. Problems of this kind are relevant for applications in engineering, chemistry and in biology like e.g. biological signal transduction. For the a posteriori error control of the coupled system, a residual error estimator is derived which takes into account the approximation errors due to the finite element discretisation in space as well as the polyhedral approximation of the surface. An adaptive refinement algorithm controls the overall error. Numerical experiments illustrate the performance of the a posteriori error estimator and the adaptive algorithm with several benchmark examples.

  • H. Antil, M. Hintermüller, R.H. Nochetto, Th.M. Surowiec, D. Wegner, Finite horizon model predictive control of electrowetting on dielectric with pinning, Interfaces and Free Boundaries. Mathematical Modelling, Analysis and Computation, 19 (2017), pp. 1--30.

  • M.H. Farshbaf Shaker, R. Henrion, D. Hömberg, Properties of chance constraints in infinite dimensions with an application to PDE constrained optimization, Set-Valued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., (2017), published online on 11.10.2017, DOI 10.1007/s11228-017-0452-5 .
    Abstract
    Chance constraints represent a popular tool for finding decisions that enforce a robust satisfaction of random inequality systems in terms of probability. They are widely used in optimization problems subject to uncertain parameters as they arise in many engineering applications. Most structural results of chance constraints (e.g., closedness, convexity, Lipschitz continuity, differentiability etc.) have been formulated in a finite-dimensional setting. The aim of this paper is to generalize some of these well-known semi-continuity and convexity properties to a setting of control problems subject to (uniform) state chance constraints.

  • V. Guigues, R. Henrion, Joint dynamic probabilistic constraints with projected linear decision rules, Optimization Methods & Software, 32 (2017), pp. 1006--1032.
    Abstract
    We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We establish the relation between the original (infinite dimensional) problem and approximating problems working with projections from different subclasses of decision policies. Considering the subclass of linear decision rules and a generalized linear model for the underlying stochastic process with noises that are Gaussian or truncated Gaussian, we show that the value and gradient of the objective and constraint functions of the approximating problems can be computed analytically.

  • W. VAN Ackooij, R. Henrion, (Sub-) Gradient formulae for probability functions of random inequality systems under Gaussian distribution, SIAM/ASA Journal on Uncertainty Quantification, 5 (2017), pp. 63--87, DOI 10.1137/16M1061308 .
    Abstract
    We consider probability functions of parameter-dependent random inequality systems under Gaussian distribution. As a main result, we provide an upper estimate for the Clarke subdifferential of such probability functions without imposing compactness conditions. A constraint qualification ensuring continuous differentiability is formulated. Explicit formulae are derived from the general result in case of linear random inequality systems. In the case of a constant coefficient matrix an upper estimate for even the smaller Mordukhovich subdifferential is proven.

  • M. Eigel, Ch. Merdon, Equilibration a posteriori error estimation for convection-diffusion-reaction problems, Journal of Scientific Computing, 67 (2016), pp. 747--768.
    Abstract
    We study a posteriori error estimates for convection-diffusion-reaction problems with possibly dominating convection or reaction and inhomogeneous boundary conditions. For the conforming FEM discretisation with streamline diffusion stabilisation (SDM), we derive robust and efficient error estimators based on the reconstruction of equilibrated fluxes in an admissible discrete subspace of H (div, Ω). Error estimators of this type have become popular recently since they provide guaranteed error bounds without further unknown constants. The estimators can be improved significantly by some postprocessing and divergence correction technique. For an extension of the energy norm by a dual norm of some part of the differential operator, complete independence from the coefficients of the problem is achieved.

    Numerical benchmarks illustrate the very good performance of the error estimators in the convection dominated and the singularly perturbed cases.

  • D. Peschka, N. Rotundo, M. Thomas, Towards doping optimization of semiconductor lasers, Journal of Computational and Theoretical Transport, 45 (2016), pp. 410--423.
    Abstract
    We discuss analytical and numerical methods for the optimization of optoelectronic devices by performing optimal control of the PDE governing the carrier transport with respect to the doping profile. First, we provide a cost functional that is a sum of a regularization and a contribution, which is motivated by the modal net gain that appears in optoelectronic models of bulk or quantum-well lasers. Then, we state a numerical discretization, for which we study optimized solutions for different regularizations and for vanishing weights.

  • M.J. Cánovas, R. Henrion, M.A. López, J. Parra, Outer limit of subdifferentials and calmness moduli in linear and nonlinear programming, Journal of Optimization Theory and Applications, 169 (2016), pp. 925--952.
    Abstract
    With a common background and motivation, the main contributions of this paper are developed in two different directions. Firstly, we are concerned with functions which are the maximum of a finite amount of continuously differentiable functions of n real variables, paying attention to the case of polyhedral functions. For these max-functions, we obtain some results about outer limits of subdifferentials, which are applied to derive an upper bound for the calmness modulus of nonlinear systems. When confined to the convex case, in addition, a lower bound on this modulus is also obtained. Secondly, by means of a KKT index set approach, we are also able to provide a point-based formula for the calmness modulus of the argmin mapping of linear programming problems without any uniqueness assumption on the optimal set. This formula still provides a lower bound in linear semi-infinite programming. Illustrative examples are given.

  • M.J. Cánovas, R. Henrion, J. Parra, F.J. Toledo, Critical objective size and calmness modulus in linear programming, Set-Valued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 24 (2016), pp. 565--579.
    Abstract
    This paper introduces the concept of critical objective size associated with a linear program in order to provide operative point-based formulas (only involving the nominal data, and not data in a neighborhood) for computing or estimating the calmness modulus of the optimal set (argmin) mapping under uniqueness of nominal optimal solution and perturbations of all coefficients. Our starting point is an upper bound on this modulus given in citeCHPTmp. In this paper we prove that this upper bound is attained if and only if the norm of the objective function coefficient vector is less than or equal to the critical objective size. This concept also allows us to obtain operative lower bounds on the calmness modulus. We analyze in detail an illustrative example in order to explore some strategies that can improve the referred upper and lower bounds.

  • C. Carstensen, M. Eigel, Reliable averaging for the primal variable in the Courant FEM and hierarchical error estimators on red-refined meshes, Computational Methods in Applied Mathematics, 16 (2016), pp. 213--230.
    Abstract
    A hierarchical a posteriori error estimator for the first-order finite element method (FEM) on a red-refined triangular mesh is presented for the 2D Poisson model problem. Reliability and efficiency with some explicit constant is proved for triangulations with inner angles smaller than or equal to pi/2. The error estimator does not rely on any saturation assumption and is valid even in the pre-asymptotic regime on arbitrarily coarse meshes. The evaluation of the estimator is a simple post-processing of the piecewise linear FEM without any extra solve plus a higher-order approximation term. The results also allows the striking observation that arbitrary local averaging of the primal variable leads to a reliable and efficient error estimation. Several numerical experiments illustrate the performance of the proposed a posteriori error estimator for computational benchmarks.

  • P. Colli, G. Gilardi, J. Sprekels, A boundary control problem for the viscous Cahn--Hilliard equation with dynamic boundary conditions, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 73 (2016), pp. 195--225.
    Abstract
    A boundary control problem for the viscous Cahn-Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved.

  • P. Colli, G. Gilardi, J. Sprekels, Constrained evolution for a quasilinear parabolic equation, Journal of Optimization Theory and Applications, 170 (2016), pp. 713--734.
    Abstract
    In the present contribution, a feedback control law is studied for a quasilinear parabolic equation. First, we prove the well-posedness and some regularity results for the Cauchy--Neumann problem for this equation, modified by adding an extra term which is a multiple of the subdifferential of the distance function from a closed convex set K of L2(Ω). Then, we consider convex sets of obstacle or double-obstacle type, and we can act on the factor of the feedback control in order to be able to reach the convex set within a finite time, by proving rigorously this property.

  • P. Colli, G. Gilardi, J. Sprekels, Distributed optimal control of a nonstandard nonlocal phase field system, AIMS Mathematics, 1 (2016), pp. 246--281.
    Abstract
    We investigate a distributed optimal control problem for a nonlocal phase field model of viscous Cahn-Hilliard type. The model constitutes a nonlocal version of a model for two-species phase segregation on an atomic lattice under the presence of diffusion that has been studied in a series of papers by P. Podio-Guidugli and the present authors. The model consists of a highly nonlinear parabolic equation coupled to an ordinary differential equation. The latter equation contains both nonlocal and singular terms that render the analysis difficult. Standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.

  • G. Colombo, R. Henrion, N.D. Hoang, B.S. Mordukhovich, Optimal control of the sweeping process over polyhedral controlled sets, Journal of Differential Equations, 260 (2016), pp. 3397--3447.
    Abstract
    The paper addresses a new class of optimal control problems governed by the dissipative and discontinuous differential inclusion of the sweeping/Moreau process while using controls to determine the best shape of moving convex polyhedra in order to optimize the given Bolza-type functional, which depends on control and state variables as well as their velocities. Besides the highly non-Lipschitzian nature of the unbounded differential inclusion of the controlled sweeping process, the optimal control problems under consideration contain intrinsic state constraints of the inequality and equality types. All of this creates serious challenges for deriving necessary optimality conditions. We develop here the method of discrete approximations and combine it with advanced tools of first-order and second-order variational analysis and generalized differentiation. This approach allows us to establish constructive necessary optimality conditions for local minimizers of the controlled sweeping process expressed entirely in terms of the problem data under fairly unrestrictive assumptions. As a by-product of the developed approach, we prove the strong W1,2-convergence of optimal solutions of discrete approximations to a given local minimizer of the continuous-time system and derive necessary optimality conditions for the discrete counterparts. The established necessary optimality conditions for the sweeping process are illustrated by several examples.

  • A. Gasnikov, P. Dvurechensky, Y. Dorn, Y. Maximov, Numerical methods for finding equilibrium flow distribution in Beckman and stable dynamics models, Rossiiskaya Akademiya Nauk. Matematicheskoe Modelirovanie, 28 (2016), pp. 40--64.

  • H. Meinlschmidt, J. Rehberg, Hölder-estimates for non-autonomous parabolic problems with rough data, Evolution Equations and Control Theory, 5 (2016), pp. 147--184.
    Abstract
    In this paper we establish Hölder estimates for solutions to non-autonomous parabolic equations on non-smooth domains which are complemented with mixed boundary conditions. The corresponding elliptic operators are of divergence type, the coefficient matrix of which depends only measurably on time. These results are in the tradition of the classical book of Ladyshenskaya et al., which also serves as the starting point for our investigations.

  • K. Sturm, M. Hintermüller, D. Hömberg, Distortion compensation as a shape optimisation problem for a sharp interface model, Computational Optimization and Applications. An International Journal, 64 (2016), pp. 557--588.
    Abstract
    We study a mechanical equilibrium problem for a material consisting of two components with different densities, which allows to change the outer shape by changing the interface between the subdomains. We formulate the shape design problem of compensating unwanted workpiece changes by controlling the interface, employ regularity results for transmission problems for a rigorous derivation of optimality conditions based on the speed method, and conclude with some numerical results based on a spline approximation of the interface.

  • M.H. Farshbaf Shaker, C. Hecht, Optimal control of elastic vector-valued Allen--Cahn variational inequalities, SIAM Journal on Control and Optimization, 54 (2016), pp. 129--152.
    Abstract
    In this paper we consider a elastic vector-valued Allen--Cahn MPCC (Mathematical Programs with Complementarity Constraints) problem. We use a regularization approach to get the optimality system for the subproblems. By passing to the limit in the optimality conditions for the regularized subproblems, we derive certain generalized first-order necessary optimality conditions for the original problem.

  • S.P. Frigeri, E. Rocca, J. Sprekels, Optimal distributed control of a nonlocal Cahn--Hilliard/Navier--Stokes system in two dimensions, SIAM Journal on Control and Optimization, 54 (2016), pp. 221 -- 250.
    Abstract
    We study a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids coupling the Navier-Stokes system with a convective nonlocal Cahn-Hilliard equation in two dimensions of space. We apply recently proved well-posedness and regularity results in order to establish existence of optimal controls as well as first-order necessary optimality conditions for an associated optimal control problem in which a distributed control is applied to the fluid flow.

  • M. Hintermüller, Th. Surowiec, A bundle-free implicit programming approach for a class of elliptic MPECs in function space, Mathematical Programming Series A, 160 (2016), pp. 271--305.

  • E. Rocca, J. Sprekels, Optimal distributed control of a nonlocal convective Cahn--Hilliard equation by the velocity in three dimensions, SIAM Journal on Control and Optimization, 53 (2015), pp. 1654--1680.
    Abstract
    In this paper we study a distributed optimal control problem for a nonlocal convective Cahn-Hilliard equation with degenerate mobility and singular potential in three dimensions of space. While the cost functional is of standard tracking type, the control problem under investigation cannot easily be treated via standard techniques for two reasons: the state system is a highly nonlinear system of PDEs containing singular and degenerating terms, and the control variable, which is given by the velocity of the motion occurring in the convective term, is nonlinearly coupled to the state variable. The latter fact makes it necessary to state rather special regularity assumptions for the admissible controls, which, while looking a bit nonstandard, are however quite natural in the corresponding analytical framework. In fact, they are indispensable prerequisites to guarantee the well-posedness of the associated state system. In this contribution, we employ recently proved existence, uniqueness and regularity results for the solution to the associated state system in order to establish the existence of optimal controls and appropriate first-order necessary optimality conditions for the optimal control problem.

  • P.-É. Druet, Some mathematical problems related to the second order optimal shape of a crystallization interface, Discrete and Continuous Dynamical Systems, 35 (2015), pp. 2443--2463.
    Abstract
    We consider the problem to optimize the stationary temperature distribution and the equilibrium shape of the solid-liquid interface in a two-phase system subject to a temperature gradient. The interface satisfies the minimization principle of the free energy, while the temperature is solving the heat equation with a radiation boundary conditions at the outer wall. Under the condition that the temperature gradient is uniformly negative in the direction of crystallization, the interface is expected to have a global graph representation. We reformulate this condition as a pointwise constraint on the gradient of the state, and we derive the first order optimality system for a class of objective functionals that account for the second surface derivatives, and for the surface temperature gradient.

  • M. Eigel, D. Peterseim, Simulation of composite materials by a Network FEM with error control, Computational Methods in Applied Mathematics, 15 (2015), pp. 21--37.
    Abstract
    A novel Finite Element Method (FEM) for the computational simulation in particle reinforced composite materials with many inclusions is presented. It is based on a specially designed mesh consisting of triangles and channel-like connections between inclusions which form a network structure. The total number of elements and, hence, the number of degrees of freedom are proportional to the number of inclusions. The error of the method is independent of the possibly tiny distances of neighbouring inclusions.

    We present algorithmic details for the generation of the problem adapted mesh and derive an efficient residual a posteriori error estimator which enables to compute reliable upper and lower error bounds. Several numerical examples illustrate the performance of the method and the error estimator. In particular, it is demonstrated that the (common) assumption of a lattice structure of inclusions can easily lead to incorrect predictions about material properties.

  • P. Colli, G. Gilardi, J. Sprekels, A boundary control problem for the pure Cahn--Hilliard equation with dynamic boundary conditions, Advances in Nonlinear Analysis, 4 (2015), pp. 311--325.
    Abstract
    A boundary control problem for the pure Cahn--Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved.

  • P. Colli, M.H. Farshbaf Shaker, G. Gilardi, J. Sprekels, Optimal boundary control of a viscous Cahn--Hilliard system with dynamic boundary condition and double obstacle potentials, SIAM Journal on Control and Optimization, 53 (2015), pp. 2696--2721.
    Abstract
    In this paper, we investigate optimal boundary control problems for Cahn--Hilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace--Beltrami operator. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. We prove existence of optimal controls and derive first-order necessary conditions of optimality. The general strategy, which follows the lines of the recent approach by Colli, Farshbaf-Shaker, Sprekels (see Appl. Math. Optim., 2014) to the (simpler) Allen--Cahn case, is the following: we use the results that were recently established by Colli, Gilardi, Sprekels in the preprint arXiv:1407.3916 [math.AP] for the case of (differentiable) logarithmic potentials and perform a so-called “deep quench limit”. Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for the case of (non-differentiable) double obstacle potentials.

  • P. Colli, M.H. Farshbaf Shaker, G. Gilardi, J. Sprekels, Second-order analysis of a boundary control problem for the viscous Cahn--Hilliard equation with dynamic boundary conditions, Annals of the Academy of Romanian Scientists. Mathematics and its Applications., 7 (2015), pp. 41--66.
    Abstract
    In this paper we establish second-order sufficient optimality conditions for a boundary control problem that has been introduced and studied by three of the authors in the preprint arXiv:1407.3916. This control problem regards the viscous Cahn--Hilliard equation with possibly singular potentials and dynamic boundary conditions.

  • P. Colli, M.H. Farshbaf Shaker, J. Sprekels, A deep quench approach to the optimal control of an Allen--Cahn equation with dynamic boundary conditions and double obstacles, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 71 (2015), pp. 1--24.
    Abstract
    In this paper, we investigate optimal control problems for Allen-Cahn variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace-Beltrami operator. The approach covers both the cases of distributed controls and of boundary controls. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. We prove existence of optimal controls and derive first-order necessary conditions of optimality. The general strategy is the following: we use the results that were recently established by two of the authors for the case of (differentiable) logarithmic potentials and perform a so-called “deep quench limit”. Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for the case of (non-differentiable) double obstacle potentials.

  • P. Colli, J. Sprekels, Optimal control of an Allen--Cahn equation with singular potentials and dynamic boundary condition, SIAM Journal on Control and Optimization, 53 (2015), pp. 213--234.
    Abstract
    In this paper, we investigate optimal control problems for Allen--Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace--Beltrami operator. The approach covers both the cases of distributed controls and of boundary controls. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. Parabolic problems with nonlinear dynamic boundary conditions involving the Laplace--Beltrami operation have recently drawn increasing attention due to their importance in applications, while their optimal control was apparently never studied before. In this paper, we first extend known well-posedness and regularity results for the state equation and then show the existence of optimal controls and that the control-to-state mapping is twice continuously Fréchet differentiable between appropriate function spaces. Based on these results, we establish the first-order necessary optimality conditions in terms of a variational inequality and the adjoint state equation, and we prove second-order sufficient optimality conditions.

  • G. Colombo, R. Henrion, N.D. Hoang, B.S. Mordukhovich, Discrete approximations of a controlled sweeping process, Set-Valued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 23 (2015), pp. 69--86.

  • W. Giese, M. Eigel, S. Westerheide, Ch. Engwer, E. Klipp, Influence of cell shape, inhomogeneities and diffusion barriers in cell polarization models, Physical Biology, 12 (2015), pp. 066014/1--066014/18.
    Abstract
    In silico experiments bear the potential to further the understanding of biological transport processes by allowing a systematic modification of any spatial property and providing immediate simulation results for the chosen models. We consider cell polarization and spatial reorganization of membrane proteins which are fundamental for cell division, chemotaxis and morphogenesis. Our computational study is motivated by mating and budding processes of S. cerevisiae. In these processes a key player during the initial phase of polarization is the GTPase Cdc42 which occurs in an active membrane-bound form and an inactive cytosolic form. We use partial differential equations to describe the membrane-cytosol shuttling of Cdc42 during budding as well as mating of yeast. The membrane is modeled as a thin layer that only allows lateral diffusion and the cytosol is modeled as a volume. We investigate how cell shape and diffusion barriers like septin structures or bud scars influence Cdc42 cluster formation and subsequent polarization of the yeast cell. Since the details of the binding kinetics of cytosolic proteins to the membrane are still controversial, we employ two conceptual models which assume different binding kinetics. An extensive set of in silico experiments with different modeling hypotheses illustrate the qualitative dependence of cell polarization on local membrane curvature, cell size and inhomogeneities on the membrane and in the cytosol. We examine that spatial inhomogenities essentially determine the location of Cdc42 cluster formation and spatial properties are crucial for the realistic description of the polarization process in cells. In particular, our computer simulations suggest that diffusion barriers are essential for the yeast cell to grow a protrusion.

  • P. Dvurechensky, Y. Nesterov, V. Spokoiny, Primal-dual methods for solving infinite-dimensional games, Journal of Optimization Theory and Applications, 166 (2015), pp. 23--51.

  • M.H. Farshbaf Shaker, Ch. Heinemann, A phase field approach for optimal boundary control of damage processes in two-dimensional viscoelastic media, Mathematical Models & Methods in Applied Sciences, 25 (2015), pp. 2749--2793.
    Abstract
    In this work we investigate a phase field model for damage processes in two-dimensional viscoelastic media with nonhomogeneous Neumann data describing external boundary forces. In the first part we establish global-in-time existence, uniqueness, a priori estimates and continuous dependence of strong solutions on the data. The main difficulty is caused by the irreversibility as well as boundedness of the phase field variable which results in a doubly constrained PDE system. In the last part we consider an optimal control problem where a cost functional penalizes maximal deviations from prescribed damage profiles. The goal is to minimize the cost functional with respect to exterior forces acting on the boundary which play the role of the control variable in the considered model . To this end, we prove existence of minimizers and study a family of “local” approximations via adapted cost functionals.

  • M.H. Farshbaf Shaker, A relaxation approach to vector-valued Allen--Cahn MPEC problems, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 72 (2015), pp. 325--351.

  • TH. Arnold, R. Henrion, A. Möller, S. Vigerske, A mixed-integer stochastic nonlinear optimization problem with joint probabilistic constraints, Pacific Journal of Optimization. An International Journal, 10 (2014), pp. 5--20.
    Abstract
    We illustrate the solution of a mixed-integer stochastic nonlinear optimization problem in an application of power management. In this application, a coupled system consisting of a hydro power station and a wind farm is considered. The objective is to satisfy the local energy demand and sell any surplus energy on a spot market for a short time horizon. Generation of wind energy is assumed to be random, so that demand satisfaction is modeled by a joint probabilistic constraint taking into account the multivariate distribution. The turbine is forced to either operate between given positive limits or to be shut down. This introduces additional binary decisions. The numerical solution procedure is presented and results are illustrated.

  • M. Eigel, T. Samrowski, Functional a posteriori error estimation for stationary reaction-convection-diffusion problems, Computational Methods in Applied Mathematics, 14 (2014), pp. 135--150.
    Abstract
    A functional type a posteriori error estimator for the finite element discretisation of the stationary reaction-convection-diffusion equation is derived. In case of dominant convection, the solution for this class of problems typically exhibits boundary layers and shock-front like areas with steep gradients. This renders the accurate numerical solution very demanding and appropriate techniques for the adaptive resolution of regions with large approximation errors are crucial. Functional error estimators as derived here contain no mesh-dependent constants and provide guaranteed error bounds for any conforming approximation. To evaluate the error estimator, a minimisation problem is solved which does not require any Galerkin orthogonality or any specific properties of the employed approximation space. Based on a set of numerical examples, we assess the performance of the new estimator and compare it with some classic a posteriori error estimators often used in practice. It is observed that the new estimator exhibits a good efficiency also with convection-dominated problem settings.

  • K. Emich, R. Henrion, W. Römisch, Conditioning of linear-quadratic two-stage stochastic optimization problems, Mathematical Programming. A Publication of the Mathematical Programming Society, 148 (2014), pp. 201--221.
    Abstract
    In this paper a condition number for linear-quadratic two-stage stochastic optimization problems is introduced as the Lipschitz modulus of the multifunction assigning to a (discrete) probability distribution the solution set of the problem. Being the outer norm of the Mordukhovich coderivative of this multifunction, the condition number can be estimated from above explicitly in terms of the problem data by applying appropriate calculus rules. Here, a chain rule for the extended partial second-order subdifferential recently proved by Mordukhovich and Rockafellar plays a crucial role. The obtained results are illustrated for the example of two-stage stochastic optimization problems with simple recourse.

  • K. Emich, R. Henrion, A simple formula for the second-order subdifferential of maximum functions, Vietnam Journal of Mathematics, 42 (2014), pp. 467--478.
    Abstract
    We derive a simple formula for the second-order subdifferential of the maximum of coordinates which allows us to construct this set immediately from its argument and the direction to which it is applied. This formula can be combined with a chain rule recently proved by Mordukhovich and Rockafellar [9] in order to derive a similarly simple formula for the extended partial second-order subdifferential of finite maxima of smooth functions. Analogous formulae can be derived immediately for the full and conventional partial second-order subdifferentials.

  • R. Hildebrand, Hessian potentials with parallel derivatives, Results in Mathematics, 65 (2014), pp. 399--413.

  • R. Hildebrand, Minimal zeros of copositive matrices, Linear Algebra and its Applications, 459 (2014), pp. 154--174.
    Abstract
    Let A be an element of the copositive cone CnCn. A zero u of A is a nonzero nonnegative vector such that uTAu=0uTAu=0. The support of u is the index set View the MathML sourcesuppu?1,?,n corresponding to the positive entries of u. A zero u of A is called minimal if there does not exist another zero v of A such that its support supp v is a strict subset of supp u . We investigate the properties of minimal zeros of copositive matrices and their supports. Special attention is devoted to copositive matrices which are irreducible with respect to the cone S+(n)S+(n) of positive semi-definite matrices, i.e., matrices which cannot be written as a sum of a copositive and a nonzero positive semi-definite matrix. We give a necessary and sufficient condition for irreducibility of a matrix A with respect to S+(n)S+(n) in terms of its minimal zeros. A similar condition is given for the irreducibility with respect to the cone NnNn of entry-wise nonnegative matrices. For n=5n=5 matrices which are irreducible with respect to both S+(5)S+(5) and N5N5 are extremal. For n=6n=6 a list of candidate combinations of supports of minimal zeros which an exceptional extremal matrix can have is provided.

  • L. Blank, M.H. Farshbaf Shaker, H. Garcke, V. Styles, Relating phase field and sharp interface approaches to structural topology optimization, ESAIM. Control, Optimisation and Calculus of Variations, 20 (2014), pp. 1025--1058.
    Abstract
    A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement.

  • W. Bleck, D. Hömberg, U. Prahl, P. Suwanpinij, N. Togobytska, Optimal control of a cooling line for production of hot rolled dual phase steel, Steel Research International, 85 (2014), pp. 1328--1333.
    Abstract
    In this article, the optimal control of a cooling line for production of dual phase steel in a hot rolling process is discussed. In order to achieve a desired dual phase steel microstructure an optimal cooling strategy has to be found. The cooling strategy should be such that a desired final distribution of ferrite in the steel slab is reached most accurately. This problem has been solved by means of mathematical control theory. The results of the optimal control of the cooling line have been verified in hot rolling experiments at the pilot hot rolling mill at the Institute for Metal Forming (IMF), TU Bergakademie Freiberg.

  • A. Fügenschuh, B. Geissler, Ch. Hayn, R. Henrion, B. Hiller, J. Humpola, Th. Koch ET AL., Mathematical optimization for challenging network planning problems in unbundled liberalized gas markets, Energy Systems, 5 (2014), pp. 449--473.

  • W. VAN Ackooij, R. Henrion, Gradient formulae for nonlinear probabilistic constraints with Gaussian and Gaussian-like distributions, SIAM Journal on Optimization, 24 (2014), pp. 1864--1889.
    Abstract
    Probabilistic constraints represent a major model of stochastic optimization. A possible approach for solving probabilistically constrained optimization problems consists in applying nonlinear programming methods. In order to do so, one has to provide sufficiently precise approximations for values and gradients of probability functions. For linear probabilistic constraints under Gaussian distribution this can be successfully done by analytically reducing these values and gradients to values of Gaussian distribution functions and computing the latter, for instance, by Genz' code. For nonlinear models one may fall back on the spherical-radial decomposition of Gaussian random vectors and apply, for instance, Deák's sampling scheme for the uniform distribution on the sphere in order to compute values of corresponding probability functions. The present paper demonstrates how the same sampling scheme can be used in order to simultaneously compute gradients of these probability functions. More precisely, we prove a formula representing these gradients in the Gaussian case as a certain integral over the sphere again. Later, the result is extended to alternative distributions with an emphasis on the multivariate Student (or T-) distribution.

  • D. Hömberg, S. Lu, K. Sakamoto, M. Yamamoto, Parameter identification in non-isothermal nucleation and growth processes, Inverse Problems. An International Journal on the Theory and Practice of Inverse Problems, Inverse Methods and Computerized Inversion of Data, 30 (2014), pp. 035003/1--035003/24.
    Abstract
    We study non-isothermal nucleation and growth phase transformations, which are described by a generalized Avrami model for the phase transition coupled with an energy balance to account for recalescence effects. The main novelty of our work is the identification of temperature dependent nucleation rates. We prove that such rates can be uniquely identified from measurements in a subdomain and apply an optimal control approach to develop a numerical strategy for its computation.

  • P. Colli, G. Gilardi, P. Podio-Guidugli, J. Sprekels, An asymptotic analysis for a nonstandard Cahn--Hilliard system with viscosity, Discrete and Continuous Dynamical Systems -- Series S, 6 (2013), pp. 353--368.
    Abstract
    This paper is concerned with a diffusion model of phase-field type, consisting of a parabolic system of two partial differential equations, interpreted as balances of microforces and microenergy, for two unknowns: the problem's order parameter $rho$ and the chemical potential $mu$; each equation includes a viscosity term -- respectively, $varepsilon,partial_tmu$ and $delta,partial_trho$ -- with $varepsilon$ and $delta$ two positive parameters; the field equations are complemented by Neumann homogeneous boundary conditions and suitable initial conditions. In a recent paper [5], we proved that this problem is well-posed and investigated the long-time behavior of its $(varepsilon,delta)-$solutions. Here we discuss the asymptotic limit of the system as $eps$ tends to 0. We prove convergence of $(varepsilon,delta)-$solutions to the corresponding solutions for the case $eps$ =0, whose long-time behavior we characterize; in the proofs, we employ compactness and monotonicity arguments.

  • K. Krumbiegel, J. Rehberg, Second order sufficient optimality conditions for parabolic optimal control problems with pointwise state constraints, SIAM Journal on Control and Optimization, 51 (2013), pp. 301--331.
    Abstract
    In this paper we study optimal control problems governed by semilinear parabolic equations where the spatial dimension is two or three. Moreover, we consider pointwise constraints on the control and on the state. We formulate first order necessary and second order sufficient optimality conditions. We make use of recent results regarding elliptic regularity and apply the concept of maximal parabolic regularity to the occurring partial differential equations.

  • R. Henrion, A. Kruger, J. Outrata, Some remarks on stability of generalized equations, Journal of Optimization Theory and Applications, 159 (2013), pp. 681--697.
    Abstract
    The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the solution map to a class of generalized equations, where the multi-valued term amounts to the regular normal cone to a (possibly nonconvex) set given by $C^2$ inequalities. Instead of the Linear Independence qualification condition, standardly used in this context, one assumes a combination of the Mangasarian-Fromovitz and the Constant Rank qualification conditions. On the basis of the obtained generalized derivatives, new optimality conditions for a class of mathematical programs with equilibrium constrains are derived, and a workable characterization of the isolated calmness of the considered solution map is provided.

  • D. Hömberg, K. Krumbiegel, J. Rehberg, Optimal control of a parabolic equation with dynamic boundary condition, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 67 (2013), pp. 3--31.
    Abstract
    We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the Robin boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an $L^p$ function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions.

  • P. Colli, G. Gilardi, P. Podio-Guidugli, J. Sprekels, Distributed optimal control of a nonstandard system of phase field equations, Continuum Mechanics and Thermodynamics, 24 (2012), pp. 437--459.
    Abstract
    We investigate a distributed optimal control problem for a phase field model of Cahn-Hilliard type. The model describes two-species phase segregation on an atomic lattice under the presence of diffusion; it has been introduced recently in [4], on the basis of the theory developed in [15], and consists of a system of two highly nonlinearly coupled PDEs. For this reason, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.

  • P. Colli, G. Gilardi, J. Sprekels, Analysis and optimal boundary control of a nonstandard system of phase field equations, Milan Journal of Mathematics, 80 (2012), pp. 119--149.
    Abstract
    We investigate a nonstandard phase field model of Cahn-Hilliard type. The model, which was introduced in Podio-Guidugli (2006), describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs. It has been studied recently in Colli, Gilardi, Podio-Guidugli, and Sprekels (2011a and b) for the case of homogeneous Neumann boundary conditions. In this paper, we investigate the case that the boundary condition for one of the unknowns of the system is of third kind and nonhomogeneous. For the resulting system, we show well-posedness, and we study optimal boundary control problems. Existence of optimal controls is shown, and the first-order necessary optimality conditions are derived. Owing to the strong nonlinear couplings in the PDE system, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional will be of standard type.

  • G. Colombo, R. Henrion, N.D. Hoang, B.S. Mordukhovich, Optimal control of the sweeping process, Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms, 19 (2012), pp. 117--159.

  • M. Gerdts, R. Henrion, D. Hömberg, Ch. Landry, Path planning and collision avoidance for robots, Numerical Algebra, Control and Optimization, 2 (2012), pp. 437--463.
    Abstract
    An optimal control problem to find the fastest collision-free trajectory of a robot surrounded by obstacles is presented. The collision avoidance is based on linear programming arguments and expressed as state constraints. The optimal control problem is solved with a sequential programming method. In order to decrease the number of unknowns and constraints a backface culling active set strategy is added to the resolution technique.

  • R. Henrion, J. Outrata, Th. Surowiec, Analysis of M-stationary points to an EPEC modeling oligopolistic competition in an electricity spot market, ESAIM. Control, Optimisation and Calculus of Variations, 18 (2012), pp. 295--317.
    Abstract
    We consider an equilibrium problem with equilibrium constraints (EPEC) as it arises from modeling competition in an electricity spot market (under ISO regulation). For a characterization of equilibrium solutions, so-called $M$-stationarity conditions are derived. This requires a structural analysis of the problem first (constraint qualifications, strong regularity). Second, the calmness property of a certain multifunction has to be verified in order to justify $M$-stationarity. Third, for stating the stationarity conditions, the co-derivative of a normal cone mapping has to be calculated. Finally, the obtained necessary conditions are made fully explicit in terms of the problem data for one typical constellation. A simple two-settlements example serves as an illustration.

  • W. Dreyer, P.-É. Druet, O. Klein, J. Sprekels, Mathematical modeling of Czochralski type growth processes for semiconductor bulk single crystals, Milan Journal of Mathematics, 80 (2012), pp. 311--332.
    Abstract
    This paper deals with the mathematical modeling and simulation of crystal growth processes by the so-called Czochralski method and related methods, which are important industrial processes to grow large bulk single crystals of semiconductor materials such as, e.,g., gallium arsenide (GaAs) or silicon (Si) from the melt. In particular, we investigate a recently developed technology in which traveling magnetic fields are applied in order to control the behavior of the turbulent melt flow. Since numerous different physical effects like electromagnetic fields, turbulent melt flows, high temperatures, heat transfer via radiation, etc., play an important role in the process, the corresponding mathematical model leads to an extremely difficult system of initial-boundary value problems for nonlinearly coupled partial differential equations. In this paper, we describe a mathematical model that is under use for the simulation of real-life growth scenarios, and we give an overview of mathematical results and numerical simulations that have been obtained for it in recent years.

  • R. Henrion, J. Outrata, Th. Surowiec, On regular coderivatives in parametric equilibria with non-unique multiplier, Mathematical Programming. A Publication of the Mathematical Programming Society, 136 (2012), pp. 111--131.

  • K. Krumbiegel, I. Neitzel, A. Rösch, Regularization error estimates for semilinear elliptic optimal control problems with pointwise state and control constraints, Computational Optimization and Applications. An International Journal, 52 (2012), pp. 181--207.
    Abstract
    In this paper a class of semilinear elliptic optimal control problem with pointwise state and control constraints is studied. A sufficient second order optimality condition and uniqueness of the dual variables are assumed for that problem. Sufficient second order optimality conditions are shown for regularized problems with small regularization parameter. Moreover, error estimates with respect to the regularization parameter are derived.

  • P.-É. Druet, O. Klein, J. Sprekels, F. Tröltzsch, I. Yousept, Optimal control of three-dimensional state-constrained induction heating problems with nonlocal radiation effects, SIAM Journal on Control and Optimization, 49 (2011), pp. 1707--1736.
    Abstract
    The paper is concerned with a class of optimal heating problems in semiconductor single crystal growth processes. To model the heating process, time-harmonic Maxwell equations are considered in the system of the state. Due to the high temperatures characterizing crystal growth, it is necessary to include nonlocal radiation boundary conditions and a temperature-dependent heat conductivity in the description of the heat transfer process. The first goal of this paper is to prove the existence and uniqueness of the solution to the state equation. The regularity analysis associated with the time harmonic Maxwell equations is also studied. In the second part of the paper, the existence and uniqueness of the solution to the corresponding linearized equation is shown. With this result at hand, the differentiability of the control-to-state mapping operator associated with the state equation is derived. Finally, based on the theoretical results, first oder necessary optimality conditions for an associated optimal control problem are established.

  • R. Henrion, Th. Surowiec, On calmness conditions in convex bilevel programming, Applicable Analysis. An International Journal, 90 (2011), pp. 951--970.
    Abstract
    In this article we compare two different calmness conditions which are widely used in the literature on bilevel programming and on mathematical programs with equilibrium constraints. In order to do so, we consider convex bilevel programming as a kind of intersection between both research areas. The so-called partial calmness concept is based on the function value approach for describing the lower level solution set. Alternatively, calmness in the sense of multifunctions may be considered for perturbations of the generalized equation representing the same lower level solution set. Both concepts allow to derive first order necessary optimality conditions via tools of generalized differentiation introduced by Mordukhovich. They are very different, however, concerning their range of applicability and the form of optimality conditions obtained. The results of this paper seem to suggest that partial calmness is considerably more restrictive than calmness of the perturbed generalized equation. This fact is also illustrated by means of a dicretized obstacle control problem.

  • R. Henrion, C. Strugarek, Convexity of chance constraints with dependent random variables: The use of copulae, International Series in Operations Research & Management Science, 163 (2011), pp. 427--439.

  • J. Sprekels, D. Tiba, Extensions of the control variational method, Control and Cybernetics, 40 (2011), pp. 1099--1108.
    Abstract
    The control variational method is a development of the variational approach, based on optimal control theory. In this work, we give an application to a variational inequality arising in mechanics and involving unilateral conditions both in the domain and on the boundary, and we explore the extension of the method to time-dependent problems.

  • A. Caboussat, Ch. Landry, J. Rappaz, Optimization problem coupled with differential equations: A numerical algorithm mixing an interior-point method and event detection, Journal of Optimization Theory and Applications, 147 (2010), pp. 141--156.

  • M.J. Fabian, R. Henrion, A.Y. Kruger, J. Outrata, Error bounds: Necessary and sufficient conditions, Set-Valued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 18 (2010), pp. 121--149.
    Abstract
    The paper presents a general classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several derivative-like objects both from the primal as well as from the dual space are used to characterize the error bound property of extended-real-valued functions on a Banach space.

  • R. Henrion, B. Mordukhovich, N.M. Nam, Second-order analysis of polyhedral systems in finite and infinite dimensions with applications to robust stability of variational inequalities, SIAM Journal on Optimization, 20 (2010), pp. 2199--2227.

  • R. Henrion, J. Outrata, Th. Surowiec, A note on the relation between strong and M-stationarity for a class of mathematical programs with equilibrium constraints, Kybernetika. The Journal of the Czech Society for Cybernetics and Information Sciences. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Prague. English., 46 (2010), pp. 423--434.
    Abstract
    In this paper, we consider the characterization of strong stationary solutions to equilibrium problems with equilibrium constraints (EPECs). Assuming that the underlying generalized equation satisfies strong regularity in the sense of Robinson, an explicit multiplier-based stationarity condition can be derived. This is applied then to an equilibrium model arising from ISO-regulated electricity spot markets.

  • R. Henrion, W. Römisch, Lipschitz and differentiability properties of quasi-concave and singular normal distribution functions, Annals of Operations Research, 177 (2010), pp. 115--125.

  • R. Henrion, A. Seeger, Inradius and circumradius of various convex cones arising in applications, Set-Valued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 18 (2010), pp. 483--511.

  • D. Hömberg, Ch. Meyer, J. Rehberg, W. Ring, Optimal control for the thermistor problem, SIAM Journal on Control and Optimization, 48 (2010), pp. 3449--3481.
    Abstract
    This paper is concerned with the state-constrained optimal control of the two-dimensional thermistor problem, a quasi-linear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Existence, uniqueness and continuity for the state system are derived by employing maximal elliptic and parabolic regularity. By similar arguments the linearized state system is discussed, while the adjoint system involving measures is investigated using a duality argument. These results allow to derive first-order necessary conditions for the optimal control problem.

  • K. Krumbiegel, Ch. Meyer, A. Rösch, A priori error analysis for linear quadratic elliptic Neumann boundary control problems with control and state constraints, SIAM Journal on Control and Optimization, 48 (2010), pp. 5108--5142.

  • K. Krumbiegel, I. Neitzel, A. Rösch, Sufficient optimality conditions for the Moreau--Yosida-type regularization concept applied to semilinear elliptic optimal control problems with pointwise state constraints, Annals of the Academy of Romanian Scientists. Mathematics and its Applications., 2 (2010), pp. 222--246.
    Abstract
    We develop sufficient optimality conditions for a Moreau-Yosida regularized optimal control problem governed by a semilinear elliptic PDE with pointwise constraints on the state and the control. We make use of the equivalence of a setting of Moreau-Yosida regularization to a special setting of the virtual control concept, for which standard second order sufficient conditions have been shown. Moreover, we compare both regularization approaches within a numerical example.

  • R. Henrion, A. Seeger, On properties of different notions of centers for convex cones, Set-Valued and Variational Analysis. Theory and Applications. Springer, Dordrecht. English., 18 (2010), pp. 205--231.

  • R. Henrion, Ch. Küchler, W. Römisch, Scenario reduction in stochastic programming with respect to discrepancy distances, Computational Optimization and Applications. An International Journal, 43 (2009), pp. 67--93.

  • R. Henrion, J. Outrata, Th. Surowiec, On the co-derivative of normal cone mappings to inequality systems, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 71 (2009), pp. 1213--1226.
    Abstract
    The paper deals with co-derivative formulae for normal cone mappings to smooth inequality systems. Both, the regular (Linear Independence Constraint Qualification satisfied) and nonregular (Mangasarian-Fromovitz Constraint Qualification satisfied) case are considered. A major part of the results relies on general transformation formulae previously obtained by Mordukhovich and Outrata. This allows to derive exact formulae for general smooth, regular and polyhedral, possibly nonregular systems. In the nonregular, nonpolyhedral case a generalized transformation formula by Mordukhovich and Outrata applies, however a major difficulty consists in checking a calmness condition of a certain multivalued mapping. The paper provides a translation of this condition in terms of much easier to verify constraint qualifications. A series of examples illustrates the use and comparison of the presented formulae.

  • D. Hömberg, D. Kern, The heat treatment of steel --- A mathematical control problem, Materialwissenschaft und Werkstofftechnik, 40 (2009), pp. 438--442.
    Abstract
    The goal of this paper is to show how the heat treatment of steel can be modelled in terms of a mathematical optimal control problem. The approach is applied to laser surface hardening and the cooling of a steel slab including mechanical effects. Finally, it is shown how the results can be utilized in industrial practice by a coupling with machine-based control.

  • D. Hömberg, N. Togobytska, M. Yamamoto, On the evaluation of dilatometer experiments, Applicable Analysis. An International Journal, 88 (2009), pp. 669--681.
    Abstract
    The goal of this paper is a mathematical investigation of dilatometer experiments to measure the kinetics of solid-solid phase transitions in steel upon cooling from the high temperature phase. Usually, the data are only used for measuring the start and end temperature of the phase transition. In the case of several coexisting product phases, lavish microscopic investigations have to be performed to obtain the resulting fractions of the different phases. In contrast, we show that the complete phase transition kinetics including the final phase fractions are uniquely determined by the dilatometer data and present some numerical identification results.

  • K. Krumbiegel, A. Rösch, A virtual control concept for state constrained optimal control problems, Computational Optimization and Applications. An International Journal, 43 (2009), pp. 213--233.

  • J. Sprekels, D. Tiba, The control variational approach for differential systems, SIAM Journal on Control and Optimization, 47 (2009), pp. 3220--3236.

  • P. Suwanpinij, N. Togobytska, Ch. Keul, W. Weiss, U. Prahl, D. Hömberg, W. Bleck, Phase transformation modeling and parameter identification from dilatometric investigations, Steel Research International, 79 (2008), pp. 793--799.
    Abstract
    The goal of this paper is to propose a new approach towards the evaluation of dilatometric results, which are often employed to analyse the phase transformation kinetics in steel, especially in terms of continuous cooling transformation (CCT) diagram. A simple task of dilatometry is deriving the start and end temperatures of the phase transformation. It can yield phase transformation kinetics provided that plenty metallographic investigations are performed, whose analysis is complicated especially in case of several coexisting product phases. The new method is based on the numerical solution of a thermomechanical identification problem. It is expected that the phase transformation kinetics can be derived by this approach with less metallographic tasks. The first results are remarkably promising although further investigations are required for the numerical simulations.

  • R. Henrion, Ch. Küchler, W. Römisch, Discrepancy distances and scenario reduction in two-stage stochastic integer programming, Journal of Industrial and Management Optimization, 4 (2008), pp. 363--384.

  • R. Henrion, J. Outrata, On calculating the normal cone to a finite union of convex polyhedra, Optimization. A Journal of Mathematical Programming and Operations Research, 57 (2008), pp. 57--78.

  • R. Henrion, A. Seeger, Uniform boundedness of norms of convex and nonconvex processes, Numerical Functional Analysis and Optimization. An International Journal, 29 (2008), pp. 551--573.

  • R. Henrion, C. Strugarek, Convexity of chance constraints with independent random variables, Computational Optimization and Applications. An International Journal, 41 (2008), pp. 263--276.

  • D. Dentcheva, R. Henrion, A. Ruszczynski, Stability and sensitivity of optimization problems with first order stochastic dominance constraints, SIAM Journal on Optimization, 18 (2007), pp. 322--337.

  • C. Lefter, J. Sprekels, Optimal boundary control of a phase field system modeling nonisothermal phase transitions, Advances in Mathematical Sciences and Applications, 17 (2007), pp. 181-194.

  • R. Henrion, W. Römisch, On M-stationary points for a stochastic equilibrium problem under equilibrium constraints in electricity spot market modeling, Applications of Mathematics, 522 (2007), pp. 473--494.
    Abstract
    Modeling several competitive leaders and followers acting in an electricity market leads to coupled systems of mathematical programs with equilibrium constraints, called equilibrium problems with equilibrium constraints (EPECs). We consider a simplified model for competition in electricity markets under uncertainty of demand in an electricity network as a (stochastic) multi-leader-follower game. First order necessary conditions are developed for the corresponding stochastic EPEC based on a result of Outrata [17]. For applying the general result an explicit representation of the co-derivative of the normal cone mapping to a polyhedron is derived (Proposition 3.2). Later the co-derivative formula is used for verifying constraint qualifications and for identifying M-stationary solutions of the stochastic EPEC if the demand is represented by a finite number of scenarios.

  • R. Henrion, Structural properties of linear probabilistic constraints, Optimization. A Journal of Mathematical Programming and Operations Research, 56 (2007), pp. 425--440.

  • R. Henrion, A. Lewis, A. Seeger, Distance to uncontrollability for convex processes, SIAM Journal on Optimization, 45 (2006), pp. 26--50.

  • R. Henrion, Some remarks on value-at-risk optimization, International Journal of Management Science and Engineering Management, 1 (2006), pp. 111--118.

  • V. Arnăutu, J. Sprekels, D. Tiba, Optimization problems for curved mechanical structures, SIAM Journal on Control and Optimization, 44 (2005), pp. 743--775.

  • R. Henrion, J. Outrata, Calmness of constraint systems with applications, Mathematical Programming. A Publication of the Mathematical Programming Society, 104 (2005), pp. 437--464.

  • P. Bosch, A. Jourani, R. Henrion, Sufficient conditions for error bounds and applications, Applied Mathematics and Optimization. An International Journal with Applications to Stochastics, 50 (2004), pp. 161--181.

  • R. Henrion, W. Römisch, Hölder and Lipschitz stability of solution sets in programs with probabilistic constraints, Mathematical Programming. A Publication of the Mathematical Programming Society, 100 (2004), pp. 589--611.

  • R. Henrion, A. Möller, Optimization of a continuous distillation process under random inflow rate, Computers & Mathematics with Applications. An International Journal, 45 (2003), pp. 247--262.

  • D. Hömberg, J. Sokolowski, Optimal shape design of inductor coils for induction hardening, SIAM Journal on Control and Optimization, 42 (2003), pp. 1087--1117.

  • D. Hömberg, S. Volkwein, Control of laser surface hardening by a reduced-order approach using proper orthogonal decomposition, Mathematical and Computer Modelling, 38 (2003), pp. 1003-1028.

  • J. Sprekels, D. Tiba, Optimization of clamped plates with discontinuous thickness, Systems & Control Letters, 48 (2003), pp. 289-295.

  • A. Ignat, J. Sprekels, D. Tiba, Analysis and optimization of nonsmooth arches, SIAM Journal on Control and Optimization, 40 (2001), pp. 1107-1133.

  • V. Arnăutu, H. Langmach, J. Sprekels, D. Tiba, On the approximation and the optimization of plates, Numerical Functional Analysis and Optimization. An International Journal, 21 (2000), pp. 337--354.

  • J. Sprekels, D. Tiba, Sur les arches lipschitziennes, Comptes Rendus Mathematique. Academie des Sciences. Paris, 331 (2000), pp. 179--184.

  Contributions to Collected Editions

  • P. Colli, J. Sprekels, Optimal boundary control of a nonstandard Cahn--Hilliard system with dynamic boundary condition and double obstacle inclusions, in: Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs: In Honour of Prof. Gianni Gilardi, P. Colli, A. Favini, E. Rocca, G. Schimperna, J. Sprekels, eds., 22 of Springer INdAM Series, Springer International Publishing, 2017, pp. 151--182, DOI 10.20347/WIAS.PREPRINT.2370 .
    Abstract
    In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by P.Podio-Guidugli in Ric. Mat. 55 (2006), pp.105-118. The model consists of a strongly coupled system of nonlinear parabolic differential inclusions, in which products between the unknown functions and their time derivatives occur that are difficult to handle analytically; the system is complemented by initial and boundary conditions. For the order parameter of the phase separation process, a dynamic boundary condition involving the Laplace-Beltrami operator is assumed, which models an additional nonconserving phase transition occurring on the surface of the domain. We complement in this paper results that were established in the recent contribution appeared in Evol. Equ. Control Theory 6 (2017), pp. 35-58, by the two authors and Gianni Gilardi. In contrast to that paper, in which differentiable potentials of logarithmic type were considered, we investigate here the (more difficult) case of nondifferentiable potentials of double obstacle type. For such nonlinearities, the standard techniques of optimal control theory to establish the existence of Lagrange multipliers for the state constraints are known to fail. To overcome these difficulties, we employ the following line of approach: we use the results contained in the preprint arXiv:1609.07046 [math.AP] (2016), pp. 1-30, for the case of (differentiable) logarithmic potentials and perform a so-called "deep quench limit". Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for the case of (nondifferentiable) double obstacle potentials.

  • P. Farrell, A. Linke, Uniform second order convergence of a complete flux scheme on nonuniform 1D grids, in: Finite Volumes for Complex Applications VIII - Methods and Theoretical Aspects FVCA 8, Lille, France, June 2017, C. Cances, P. Omnes, eds., 199 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2017, pp. 303--310.

  • A. Anikin, A. Gasnikov, A. Garinov, P. Dvurechensky, V. Semenov, Parallelizable dual methods for searching equilibriums in large-scale mixed traffic assignment problems (in Russian), in: Proceedings of Information Technology and Systems 2016 -- The 40th Interdisciplinary Conference & School, Institute for Information Transmission Problems (Kharkevich Institute), Moscow, 2016, pp. 85--89.

  • A. Chernov, P. Dvurechensky, A primal-dual first-order method for minimization problems with linear constraints, in: Proceedings of Information Technology and Systems 2016 -- The 40th Interdisciplinary Conference & School, Institute for Information Transmission Problems (Kharkevich Institute), Moscow, 2016, pp. 41--45.

  • P. Dvurechensky, A. Gasnikov, E. Gasnikova, S. Matsievsky, A. Rodomanov, I. Usik, Primal-dual method for searching equilibrium in hierarchical congestion population games, in: Supplementary Proceedings of the 9th International Conference on Discrete Optimization and Operations Research and Scientific School (DOOR 2016), A. Kononov, I. Bykadorov , O. Khamisov , I. Davydov , P. Kononova , eds., 1623 of CEUR Workshop Proceedings, Technische Universität Aaachen, pp. 584--595.

  • CH. Landry, M. Gerdts, R. Henrion, D. Hömberg, W. Welz, Collision-free path planning of welding robots, in: Progress in Industrial Mathematics at ECMI 2012, M. Fontes, M. Günther, N. Marheineke, eds., 19 of Mathematics in Industry, Springer, Cham et al., 2014, pp. 251--256.

  • L. Blank, M.H. Farshbaf Shaker, C. Hecht, J. Michl, Ch. Rupprecht, Optimal control of Allen--Cahn systems, in: Trends in PDE Constrained Optimization, G. Leugering, P. Benner ET AL., eds., 165 of International Series of Numerical Mathematics, Birkhäuser, Basel et al., 2014, pp. 11--26.

  • L. Blank, M.H. Farshbaf Shaker, H. Garcke, Ch. Rupprecht, V. Styles, Multi-material phase field approach to structural topology optimization, in: Trends in PDE Constrained Optimization, G. Leugering, P. Benner ET AL., eds., 165 of International Series of Numerical Mathematics, Birkhäuser, Basel et al., 2014, pp. 231--246.

  • T. Bosse, R. Henrion, D. Hömberg, Ch. Landry, H. Leövey ET AL., C2 -- Nonlinear programming with applications to production processes, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 171--187.

  • C. Carstensen, M. Hintermüller, D. Hömberg, F. Tröltzsch, C -- Production, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 151--153.

  • M. Hintermüller, D. Hömberg, O. Klein, J. Sprekels, F. Tröltzsch, C4 -- PDE-constrained optimization with industrial applications, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 207--222.

  • D. Hömberg, S. Lu, K. Sakamoto, M. Yamamoto, Nucleation rate identification in binary phase transition, in: The Impact of Applications on Mathematics -- Proceedings of the Forum of Mathematics for Industry 2013, M. Wakayama, ed., 1 of Mathematics for Industry, Springer, Tokyo et al., 2014, pp. 227--243.

  • O. Klein, J. Sprekels, SHOWCASE 13 -- Growth of semiconductor bulk single crystals, in: MATHEON -- Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 224--225.

  • CH. Landry, W. Welz, R. Henrion, D. Hömberg, M. Skutella, Task assignment, sequencing and path-planning in robotic welding cells, Methods and Models in Automation and Robotics (MMAR), 2013 -- 18th International Conference on, Miedzyzdroje, Poland, August 26 - 29, 2013, IEEE, 2013, pp. 252--257.
    Abstract
    A workcell composed of a workpiece and several welding robots is considered. We are interested in minimizing the makespan in the workcell. Hence, one needs i) to assign tasks between the robots, ii) to do the sequencing of the tasks for each robot and iii) to compute the fastest collision-free paths between the tasks. Up to now, task assignment and path-planning were always handled separately, the former being a typical Vehicle Routing Problem whereas the later is modelled using an optimal control problem. In this paper, we present a complete algorithm which combines discrete optimization techniques with collision detection and optimal control problems efficiently.

  • K. Chełminski, D. Hömberg, O. Rott, Coupling of process, machine, and work-piece in production processes: A challenge for industrial mathematics, Warsaw Seminar in Industrial Mathematics (WSIM'10), March 18 - 19, 2010, P. Grzegorzewski, T. Rzeżuchowski, eds., Issues in Industrial Mathematics, Politechnika Warszawa, 2013, pp. 57--75.

  • D. Hömberg, D. Kern, PDE-constrained control problems related to the heat treatment of steel, Warsaw Seminar in Industrial Mathematics (WSIM'10), March 18 - 19, 2010, P. Grzegorzewski, T. Rzeżuchowski, eds., Issues in Industrial Mathematics, Politechnika Warszawa, 2013, pp. 35--46.

  • M.J. Fabian, R. Henrion, A. Kruger, J. Outrata, About error bounds in metric spaces, D. Klatte, H.-J. Lüthi, K. Schmedders, eds., Operations Research Proceedings 2011, Springer, Berlin Heidelberg, 2012, pp. 33--38.

  • R. Henrion, Optimization under uncertainty (Models and basic properties), in: Wiley Encyclopedia of Operations Research and Management Science, J.J. Cochran, L.A. Cox, P. Keskinocak ET AL., eds., 5, Wiley, New York, 2011, pp. 3334--3341.

  • D. Kern, Die Welt des Herrn Kuhn, in: Besser als Mathe --- Moderne angewandte Mathematik aus dem MATHEON zum Mitmachen, K. Biermann, M. Grötschel, B. Lutz-Westphal, eds., Reihe: Populär, Vieweg+Teubner, Wiesbaden, 2010, pp. 141--150.

  • H. Heitsch, R. Henrion, Ch. Küchler, W. Römisch, Generierung von Szenariobäumen und Szenarioreduktion für stochastische Optimierungsprobleme in der Energiewirtschaft, in: Dezentrale regenerative Energieversorgung: Innovative Modellierung und Optimierung, R. Schultz, H.-J. Wagner, eds., LIT Verlag, Münster, 2009, pp. 227--254.

  • D. Hömberg, D. Kern, The heat treatment of steel --- A mathematical control problem, in: Proceedings of the 2nd International Conference on Distortion Engineering -- IDE 2008, 17--19 September 2008, Bremen, Germany, H.-W. Zoch, Th. Lübben, eds., IWT, Bremen, 2008, pp. 201--209.

  • CH. Meyer, D. Hömberg, J. Rehberg, W. Ring, Optimal control of the thermistor problem, in: Optimal Control of Coupled Systems of PDE, Workshop, March 2--8, 2008, 5 of Oberwolfach Reports, Mathematisches Forschungsinstitut Oberwolfach, 2008, pp. 624-626.

  • D. Hömberg, D. Kern, W. Weiss, Die Wärmebehandlung von Stahl --- ein Optimierungsproblem, in: Distortion Engineering -- Verzugsbeherrschung in der Fertigung III --, 3 of Sonderforschungsbereich 570, Universität Bremen, Kolloquium, 2006, pp. 39--55.

  • J. Sprekels, D. Tiba, Chapter 18: Optimal Design of Mechanical Structures, in: Control Theory of Partial Differential Equations (proceedings of the conference held at Georgetown University, May 30 -- June 1, 2003), O. Imanuvilov, G. Leugering, R. Triggiani, B. Zhang, eds., 242 of Lecture Notes in Pure and Applied Mathematics, Chapman & Hall / CRC, Boca Raton, Florida, 2005, pp. 259-271.

  • R. Henrion, Perturbation analysis of chance-constrained programs under variation of all constraint data, in: Dynamic Stochastic Optimization, K. Marti, ed., 532 of Lecture Notes in Economics and Mathematical Systems, Springer, Heidelberg, 2004, pp. 257--274.

  • D. Hömberg, S. Volkwein, W. Weiss, Optimal control strategies for the surface hardening of steel, in: Proceedings of the 2nd International Conference on Thermal Process Modelling and Computer Simulation, S. Denis, P. Archambault, J.-M. Bergheau, R. Fortunier, eds., 120 of J. Physique IV, EDP Sciences, 2004, pp. 325--335.

  • J. Sprekels, O. Klein, P. Philip, K. Wilmanski, Optimal control of sublimation growth of SiC crystals, in: Mathematics --- Key Technology for the Future. Joint Projects Between Universities and Industry, W. Jäger, H.-J. Krebs, eds., Springer, Berlin [u.a.], 2003, pp. 334--343.

  • J. Sprekels, D. Tiba, Optimization of differential systems with hysteresis, in: Analysis and Optimization of Differential Systems, IFIP TC7/WG7.2 International Working Conference on Analysis and Optimization of Differential Systems, September 10--14, 2002, Constanta, Romania, V. Barbu, I. Lasiecka, D. Tiba, C. Varsan, eds., Kluwer Academic Publishers, Boston, 2003, pp. 387--398.

  • J. Sprekels, D. Tiba, Control variational methods for differential equations, in: Optimal Control of Complex Structures, K.-H. Hoffmann, I. Lasiecka, G. Leugering, J.a.T.F. Sprekels, eds., 139 of International Series of Numerical Mathematics, Birkhäuser, Basel Boston Berlin, 2002, pp. 245-257.

  Preprints, Reports, Technical Reports

  • M. Hintermüller, N. Strogies, On the consistency of Runge--Kutta methods up to order three applied to the optimal control of scalar conservation laws, Preprint no. 2442, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2442 .
    Abstract, PDF (552 kByte)
    Higher-order Runge-Kutta (RK) time discretization methods for the optimal control of scalar conservation laws are analyzed and numerically tested. The hyperbolic nature of the state system introduces specific requirements on discretization schemes such that the discrete adjoint states associated with the control problem converge as well. Moreover, conditions on the RK-coefficients are derived that coincide with those characterizing strong stability preserving Runge-Kutta methods. As a consequence, the optimal order for the adjoint state is limited, e.g., to two even in the case where the conservation law is discretized by a third-order method. Finally, numerical tests for controlling Burgers equation validate the theoretical results.

  • P. Colli, G. Gilardi, J. Sprekels, Optimal velocity control of a convective Cahn--Hilliard system with double obstacles and dynamic boundary conditions: A `deep quench' approach, Preprint no. 2428, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2428 .
    Abstract, PDF (257 kByte)
    In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn-Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an incompressible fluid in a container and, at the same time, on the container boundary. The cost functional is of standard tracking type, while the control is exerted by the velocity of the fluid in the bulk. In this way, the coupling between the state (given by the associated order parameter and chemical potential) and control variables in the governing system of nonlinear partial differential equations is bilinear, which presents a difficulty for the analysis. In contrast to the previous paper Optimal velocity control of a viscous Cahn-Hilliard system with convection and dynamic boundary conditions by the same authors, the bulk and surface free energies are of double obstacle type, which renders the state constraint nondifferentiable. It is well known that for such cases standard constraint qualifications are not satisfied so that standard methods do not apply to yield the existence of Lagrange multipliers. In this paper, we overcome this difficulty by taking advantage of results established in the quoted paper for logarithmic nonlinearities, using a so-called `deep quench approximation'. We derive results concerning the existence of optimal controls and the first-order necessary optimality conditions in terms of a variational inequality and the associated adjoint system.

  • P. Colli, G. Gilardi, J. Sprekels, Optimal velocity control of a viscous Cahn--Hilliard system with convection and dynamic boundary conditions, Preprint no. 2427, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2427 .
    Abstract, PDF (306 kByte)
    In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn--Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an incompressible fluid in a container and, at the same time, on the container boundary. The cost functional is of standard tracking type, while the control is exerted by the velocity of the fluid in the bulk. In this way, the coupling between the state (given by the associated order parameter and chemical potential) and control variables in the governing system of nonlinear partial differential equations is bilinear, which presents an additional difficulty for the analysis. The nonlinearities in the bulk and surface free energies are of logarithmic type, which entails that the thermodynamic forces driving the phase separation process may become singular. We show existence for the optimal control problem under investigation, prove the Fréchet differentiability of the associated control-to-state mapping in suitable Banach spaces, and derive the first-order necessary optimality conditions in terms of a variational inequality and the associated adjoint system. Due to the strong nonlinear couplings between state variables and control, the corresponding proofs require a considerable analytical effort.

  • L. Adam, M. Hintermüller, Th.M. Surowiec, A PDE-constrained optimization approach for topology optimization of strained photonic devices, Preprint no. 2377, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2377 .
    Abstract, PDF (936 kByte)
    Recent studies have demonstrated the potential of using tensile-strained, doped Germanium as a means of developing an integrated light source for (amongst other things) future microprocessors. In this work, a multi-material phase-field approach to determine the optimal material configuration within a so-called Germanium-on-Silicon microbridge is considered. Here, an “optimal" configuration is one in which the strain in a predetermined minimal optical cavity within the Germanium is maximized according to an appropriately chosen objective functional. Due to manufacturing requirements, the emphasis here is on the cross-section of the device; i.e. a socalled aperture design. Here, the optimization is modeled as a non-linear optimization problem with partial differential equation (PDE) and manufacturing constraints. The resulting problem is analyzed and solved numerically. The theory portion includes a proof of existence of an optimal topology, differential sensitivity analysis of the displacement with respect to the topology, and the derivation of first and second-order optimality conditions. For the numerical experiments, an array of first and second-order solution algorithms in function-space are adapted to the current setting, tested, and compared. The numerical examples yield designs for which a significant increase in strain (as compared to an intuitive empirical design) is observed.

  • M. Hintermüller, S. Rösel, Duality results and regularization schemes for Prandtl--Reuss perfect plasticity, Preprint no. 2376, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2376 .
    Abstract, PDF (353 kByte)
    We consider the time-discretized problem of the quasi-static evolution problem in perfect plasticity posed in a non-reflexive Banach space and we derive an equivalent version in a reflexive Banach space. A primal-dual stabilization scheme is shown to be consistent with the initial problem. As a consequence, not only stresses, but also displacement and strains are shown to converge to a solution of the original problem in a suitable topology. This scheme gives rise to a well-defined Fenchel dual problem which is a modification of the usual stress problem in perfect plasticity. The dual problem has a simpler structure and turns out to be well-suited for numerical purposes. For the corresponding subproblems an efficient algorithmic approach in the infinite-dimensional setting based on the semismooth Newton method is proposed.

  • M. Eigel, J. Neumann, R. Schneider, S. Wolf, Stochastic topology optimisation with hierarchical tensor reconstruction, Preprint no. 2362, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2362 .
    Abstract, PDF (8552 kByte)
    A novel approach for risk-averse structural topology optimization under uncertainties is presented which takes into account random material properties and random forces. For the distribution of material, a phase field approach is employed which allows for arbitrary topological changes during optimization. The state equation is assumed to be a high-dimensional PDE parametrized in a (finite) set of random variables. For the examined case, linearized elasticity with a parametric elasticity tensor is used. Instead of an optimization with respect to the expectation of the involved random fields, for practical purposes it is important to design structures which are also robust in case of events that are not the most frequent. As a common risk-aware measure, the Conditional Value at Risk (CVaR) is used in the cost functional during the minimization procedure. Since the treatment of such high-dimensional problems is a numerically challenging task, a representation in the modern hierarchical tensor train format is proposed. In order to obtain this highly efficient representation of the solution of the random state equation, a tensor completion algorithm is employed which only required the pointwise evaluation of solution realizations. The new method is illustrated with numerical examples and compared with a classical Monte Carlo sampling approach.

  • L. Adam, M. Hintermüller, Th.M. Surowiec, A semismooth Newton method with analytical path-following for the $H^1$-projection onto the Gibbs simplex, Preprint no. 2340, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2340 .
    Abstract, PDF (1345 kByte)
    An efficient, function-space-based second-order method for the $H^1$-projection onto the Gibbs-simplex is presented. The method makes use of the theory of semismooth Newton methods in function spaces as well as Moreau-Yosida regularization and techniques from parametric optimization. A path-following technique is considered for the regularization parameter updates. A rigorous first and second-order sensitivity analysis of the value function for the regularized problem is provided to justify the update scheme. The viability of the algorithm is then demonstrated for two applications found in the literature: binary image inpainting and labeled data classification. In both cases, the algorithm exhibits mesh-independent behavior.

  • M. Hintermüller, C.N. Rautenberg, S. Rösel, Density of convex intersections and applications, Preprint no. 2333, WIAS, Berlin, 2016.
    Abstract, PDF (361 kByte)
    In this paper we address density properties of intersections of convex sets in several function spaces. Using the concept of Gamma-convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified. The results are further discussed in the context of finite element discretizations of sets associated to convex constraints. Finally, two applications are provided, which include elasto-plasticity and image restoration problems.

  • M. Hintermüller, M. Hinze, Ch. Kahle, T. Keil, A goal-oriented dual-weighted adaptive finite element approach for the optimal control of a nonsmooth Cahn--Hilliard--Navier--Stokes system, Preprint no. 2311, WIAS, Berlin, 2016.
    Abstract, PDF (640 kByte)
    This paper is concerned with the development and implementation of an adaptive solution algorithm for the optimal control of a time-discrete Cahn--Hilliard--Navier--Stokes system with variable densities. The free energy density associated to the Cahn--Hilliard system incorporates the double-obstacle potential which yields an optimal control problem for a family of coupled systems in each time instant of a variational inequality of fourth order and the Navier--Stokes equation. A dual-weighed residual approach for goal-oriented adaptive finite elements is presented which is based on the concept of C-stationarity. The overall error representation depends on primal residual weighted by approximate dual quantities and vice versa as well as various complementary mismatch errors. Details on the numerical realization of the adaptive concept and a report on numerical tests are given.

  • P. Colli, G. Gilardi, J. Sprekels, Optimal boundary control of a nonstandard viscous Cahn--Hilliard system with dynamic boundary condition, Preprint no. 2307, WIAS, Berlin, 2016.
    Abstract, PDF (347 kByte)
    In this paper, we study an optimal boundary control problem for a model for phase separation taking place in a spatial domain that was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly coupled system of nonlinear parabolic differential equations, in which products between the unknown functions and their time derivatives occur that are difficult to handle analytically. In contrast to the existing control literature about this PDE system, we consider here a dynamic boundary condition involving the Laplace-Beltrami operator for the order parameter of the system, which models an additional nonconserving phase transition occurring on the surface of the domain. We show the Fr&aecute;chenett differentiability of the associated control-to-state operator in appropriate Banach spaces and derive results on the existence of optimal controls and on first-order necessary optimality conditions in terms of a variational inequality and the adjoint state system.

  • M. Hintermüller, C.N. Rautenberg, M. Mohammadi, M. Kanitsar, Optimal sensor placement: A robust approach, Preprint no. 2287, WIAS, Berlin, 2016.
    Abstract, PDF (4835 kByte)
    We address the problem of optimally placing sensor networks for convection-diffusion processes where the convective part is perturbed. The problem is formulated as an optimal control problem where the integral Riccati equation is a constraint and the design variables are sensor locations. The objective functional involves a term associated to the trace of the solution to the Riccati equation and a term given by a constrained optimization problem for the directional derivative of the previous quantity over a set of admissible perturbations. The paper addresses the existence of the derivative with respect to the convective part of the solution to the Riccati equation, the well-posedness of the optimization problem and finalizes with a range of numerical tests.

  • H. Egger, Th. Kugler, N. Strogies, Parameter identification in a semilinear hyperbolic system, Preprint no. 2278, WIAS, Berlin, 2016.
    Abstract, PDF (424 kByte)
    We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and contraction arguments. We then investigate the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be ill-posed and a variational regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized solutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings.

  • M.H. Farshbaf Shaker, Ch. Heinemann, Necessary conditions of first-order for an optimal boundary control problem for viscous damage processes in 2D, Preprint no. 2269, WIAS, Berlin, 2016.
    Abstract, PDF (464 kByte)
    Controlling the growth of material damage is an important engineering task with plenty of real world applications. In this paper we approach this topic from the mathematical point of view by investigating an optimal boundary control problem for a damage phase-field model for viscoelastic media. We consider non-homogeneous Neumann data for the displacement field which describe external boundary forces and act as control variable. The underlying hyberbolic-parabolic PDE system for the state variables exhibit highly nonlinear terms which emerge in context with damage processes. The cost functional is of tracking type, and constraints for the control variable are prescribed. Based on recent results from [M. H. Farshbaf-Shaker, C. Heinemann: A phase field approach for optimal boundary control of damage processes in two-dimensional viscoelastic media. Math. Models Methods Appl. Sci. 25 (2015), 2749--2793], where global-in-time well-posedness of strong solutions to the lower level problem and existence of optimal controls of the upper level problem have been established, we show in this contribution differentiability of the control-to-state mapping, well-posedness of the linearization and existence of solutions of the adjoint state system. Due to the highly nonlinear nature of the state system which has by our knowledge not been considered for optimal control problems in the literature, we present a very weak formulation and estimation techniques of the associated adjoint system. For mathematical reasons the analysis is restricted here to the two-dimensional case. We conclude our results with first-order necessary optimality conditions in terms of a variational inequality together with PDEs for the state and adjoint state system.

  • M. Eigel, K. Sturm, Reproducing kernel Hilbert spaces and variable metric algorithms in PDE constrained shape optimisation, Preprint no. 2244, WIAS, Berlin, 2016, DOI 10.20347/WIAS.PREPRINT.2244 .
    Abstract, PDF (6274 kByte)
    In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape optimisation problems. We show that radial kernels provide convenient formulas for the shape gradient that can be efficiently used in numerical simulations. The shape gradients associated with radial kernels depend on a so called smoothing parameter that allows a smoothness adjustment of the shape during the optimisation process. Besides, this smoothing parameter can be used to modify the movement of the shape. The theoretical findings are verified in a number of numerical experiments.

  • H. Meinlschmidt, Ch. Meyer, J. Rehberg, Optimal control of the thermistor problem in three spatial dimensions, Preprint no. 2238, WIAS, Berlin, 2016.
    Abstract, PDF (14 MByte)
    This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Local existence, uniqueness and continuity for the state system are derived by employing maximal parabolic regularity in the fundamental theorem of Prüss. Global solutions are addressed, which includes analysis of the linearized state system via maximal parabolic regularity, and existence of optimal controls is shown if the temperature gradient is under control. The adjoint system involving measures is investigated using a duality argument. These results allow to derive first-order necessary conditions for the optimal control problem in form of a qualified optimality system. The theoretical findings are illustrated by numerical results.

  • L. Adam, R. Henrion, J. Outrata, On M-stationarity conditions in MPECs and the associated qualification conditions, Preprint no. 2215, WIAS, Berlin, 2016.
    Abstract, PDF (258 kByte)
    Depending on whether a mathematical program with equilibrium constraints (MPEC) is considered in its original or its enhanced (via KKT conditions) form, the assumed constraint qualifications (CQs) as well as the derived necessary optimality conditions may differ significantly. In this paper, we study this issue when imposing one of the weakest possible CQs, namely the calmness of the perturbation mapping associated with the respective generalized equations in both forms of the MPEC. It is well known that the calmness property allows one to derive so-called M-stationarity conditions. The strength of assumptions and conclusions in the two forms of the MPEC is strongly related with the CQs on the 'lower level' imposed on the set whose normal cone appears in the generalized equation. For instance, under just the Mangasarian-Fromovitz CQ (a minimum assumption required for this set), the calmness properties of the original and the enhanced perturbation mapping are drastically different. They become identical in the case of a polyhedral set or when adding the Full Rank CQ. On the other hand, the resulting optimality conditions are affected too. If the considered set even satisfies the Linear Independence CQ, both the calmness assumption and the derived optimality conditions are fully equivalent for the original and the enhanced form of the MPEC. A compilation of practically relevant consequences of our analysis in the derivation of necessary optimality conditions is provided in the main Theorem 4.3. The obtained results are finally applied to MPECs with structured equilibria.

  • CH. Heinemann, K. Sturm, Shape optimisation for a class of semilinear variational inequalities with applications to damage models, Preprint no. 2209, WIAS, Berlin, 2016.
    Abstract, PDF (590 kByte)
    The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an abstract operator setting where the operators are defined on polyhedral subsets of reflexive Banach spaces. The results are then refined for variational inequalities arising from minimisation problems for certain convex energy functionals considered over upper obstacle sets in $H^1$. One particularity is that we allow for dynamic obstacle functions which may arise from another optimisation problems. We prove a strong convergence property for the material derivative and establish state-shape derivatives under regularity assumptions. Finally, as a concrete application from continuum mechanics, we show how the dynamic obstacle case can be used to treat shape optimisation problems for time-discretised brittle damage models for elastic solids. We derive a necessary optimality system for optimal shapes whose state variables approximate desired damage patterns and/or displacement fields.

  Talks, Poster

  • A. Alphonse, Optimal control of elliptic and parabolic quasi-variational inequalities, Annual Meeting of the DFG Priority Programme 1962, October 9 - 11, 2017, Kremmen (Sommerfeld), October 10, 2017.

  • T. Keil, Simulation and control of a nonsmooth Cahn--Hilliard Navier--Stokes system with variable fluid densities (with Carmen Graessle), Annual Meeting of the DFG Priority Programme 1962, October 9 - 11, 2017, Kremmen (Sommerfeld), October 11, 2017.

  • T. Keil, Strong stationarity conditions for the optimal control of a Cahn--Hilliard--Navier--Stokes system, 14th International Conference on Free Boundary Problems: Theory and Applications, Theme Session 8 ``Optimization and Control of Interfaces'', July 9 - 14, 2017, Shanghai Jiao Tong University, China, July 10, 2017.

  • S.-M. Stengl, Generalized Nash equilibrium problems with partial differential operators: Theory, algorithms and risk aversion (with Deborah Gahururu), Annual Meeting of the DFG Priority Programme 1962, October 9 - 11, 2017, Kremmen (Sommerfeld), October 9, 2017.

  • J. Sprekels, Optimal control of PDEs: From basic principles to hard applications, International School ``Frontiers in Partial Differential Equations and Solvers'', May 22 - 26, 2017, University of Pavia, Department of Mathematics, Italy.

  • C. Löbhard, A function space based solution method with space-time adaptivity for parabolic optimal control problems with state constraints, PGMO Days 2017, November 13 - 14, 2017, EDF Lab Paris Saclay, France, November 14, 2017.

  • C. Löbhard, An adaptive space-time discretization for parabolic optimal control problem with state constraints, Joint Research Seminar on Mathematical Optimization / Non-smooth Variational Problems and Operator Equations, WIAS, Berlin, June 22, 2017.

  • C. Löbhard, An ddaptive discontinuous Galerkin method for a parabolic optimal control problem with state constraints . . ., Workshop on Optimization of Infinite Dimensional Non-Smooth Distributed Parameter Systems, October 4 - 6, 2017, Darmstadt, October 4, 2017.

  • C. Löbhard, Space-time discretization of a parabolic optimal control problem with state constraints, 18th French-German-Italian Conference on Optimization, September 25 - 28, 2017, Paderborn, September 26, 2017.

  • R. Henrion, Contraintes en probabilité: Formules du gradient et applications, Workshop ``MAS-MODE 2017", Institut Henri Poincaré, Paris, France, January 9, 2017.

  • R. Henrion, On M-stationnary condition for a simple electricity spot market model, Workshop ``Variational Analysis and Applications for Modelling of Energy Exchange'', May 4 - 5, 2017, Université Perpignan, France, May 4, 2017.

  • R. Henrion, Problèmes d'optimisation sous contraintes en probabilité, Université de Bourgogne, Département de Mathématiques, Dijon, France, October 25, 2017.

  • M. Hintermüller, (Pre)Dualization, dense embeddings of convex sets, and applications in image processing, HCM Workshop: Nonsmooth Optimization and its Applications, May 15 - 19, 2017, Hausdorff Center for Mathematics, Bonn, May 15, 2017.

  • M. Hintermüller, Adaptive finite element solvers for MPECs in function space, SIAM Conference on Optimization, Minisymposium MS122 ``Recent Trends in PDE- Constrained Optimization'', May 22 - 25, 2017, Vancouver, British Columbia, Canada, May 25, 2017.

  • M. Hintermüller, Bilevel optimization and applications in imaging, Workshop ``Emerging Developments in Interfaces and Free Boundaries'', January 22 - 28, 2017, Mathematisches Forschungsinstitut Oberwolfach.

  • M. Hintermüller, Bilevel optimization and applications in imaging, Mathematisches Kolloquium, Universität Wien, Austria, January 18, 2017.

  • M. Hintermüller, Bilevel optimization and some ``parameter learning'' applications in image processing, LMS Workshop ``Variational Methods Meet Machine Learning'', September 18, 2017, University of Cambridge, Centre for Mathematical Sciences, UK, September 18, 2017.

  • M. Hintermüller, Generalized Nash equilibrium problems in Banach spaces: Theory, Nikaido--Isoda-based path-following methods, and applications, The Third International Conference on Engineering and Computational Mathematics (ECM2017), Stream 3 ``Computational Optimization'', May 31 - June 2, 2017, The Hong Kong Polytechnic University, China, June 2, 2017.

  • M. Hintermüller, Generalized Nash games with partial differential equations, Kolloquium Arbeitsgruppe Modellierung, Numerik, Differentialgleichungen, Technische Universität Berlin, June 20, 2017.

  • M. Hintermüller, Non-smooth structures in PDE-constrained optimization, Mathematisches Kolloquium, Universität Duisburg-Essen, Fakultät für Mathematik, Essen, January 11, 2017.

  • M. Hintermüller, Nonsmooth structures in PDE constrained optimization, Optimization Seminar, Chinese Academy of Sciences, State Key Laboratory of Scientific and Engineering Computing, Beijing, China, June 6, 2017.

  • M. Hintermüller, On (pre)dualization, dense embeddings of convex sets, and applications in image processing, Isaac Newton Institute, Cambridge, UK, August 30, 2017.

  • M. Hintermüller, On (pre)dualization, dense embeddings of convex sets, and applications in image processing, University College London, Centre for Inverse Problems, UK, October 27, 2017.

  • M. Hintermüller, Optimal control of multiphase fluids and droplets, Kolloquium, Friedrich-Alexander-Universität Erlangen-Nürnberg, Department Mathematik, Erlangen, May 2, 2017.

  • M. Hintermüller, Optimal control of multiphase fluids based on non smooth models, 14th International Conference on Free Boundary Problems: Theory and Applications, Theme Session 8 ``Optimization and Control of Interfaces'', July 9 - 14, 2017, Shanghai Jiao Tong University, China, July 10, 2017.

  • M. Hintermüller, Optimal control of nonsmooth phase-field models, DFG-AIMS Workshop on ``Shape Optimization, Homogenization and Control'', March 13 - 16, 2017, Mbour, Senegal, March 14, 2017.

  • M. Hintermüller, Recent trends in PDE-constrained optimization with non-smooth structures, Fourth Conference on Numerical Analysis and Optimization (NAOIV-2017), January 2 - 5, 2017, Sultan Qaboos University, Muscat, Oman, January 4, 2017.

  • M. Hintermüller, Total variation diminishing Runge--Kutta methods for the optimal control of conservation laws: Stability and order-conditions, SIAM Conference on Optimization, Minisymposium MS111 ``Optimization with Balance Laws on Graphs'', May 22 - 25, 2017, Vancouver, British Columbia, Canada, May 25, 2017.

  • J. Neumann, The phase field approach for topology optimization under uncertainties, ZIB Computational Medicine and Numerical Mathematics Seminar, Konrad-Zuse-Zentrum für Informationstechnik Berlin, August 25, 2016.

  • TH. Petzold, The MIMESIS project -- An example for an interdisciplinary research project, Leibniz-Kolleg for Young Researchers: Chances and Challenges of Interdisciplinary Research, Thematic Workshop ``Models and Modelling'', November 9 - 11, 2016, Leibniz-Gemeinschaft, Berlin, November 9, 2016.

  • P. Dvurechensky, Accelerated primal-dual gradient method for composite optimization with unknown smoothness parameter, VIII Moscow International Conference on Operations Research (ORM2016), November 18 - 21, 2016, Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics, Russian Federation, October 19, 2016.

  • P. Dvurechensky, Accelerated primal-dual gradient method for linearly constrained minimization Problems, VII International Conference Optimization and Applications, September 25 - 28, 2016, Montenegrin Academy of Sciences and Arts, University of Montenegro, Dorodnicyn Computing Centre of FRC "Computer Science and Control" of Russian Academy of Sciences, University of Evora, Portugal, Moscow Institute of Physics and Technology, Russiate of Physics and Technology, University of Montenegro, Dorodnicyn Computing Centre of FRC "Computer Science and Control" of Russian Academy of Science, Petrovac, Montenegro, September 26, 2016.

  • M.H. Farshbaf Shaker, A phase field approach for optimal boundary control of damage processes in two-dimensional viscoelastic media, International INdAM Conference ``Optimal Control for Evolutionary PDEs and Related Topics (OCERTO 2016)'', June 20 - 24, 2016, Cortona, Italy, June 21, 2016.

  • M.H. Farshbaf Shaker, Allen--Cahn MPECs, WIAS-PGMO Workshop on Nonsmooth and Stochastic Optimization with Applications to Energy Management, May 10 - 12, 2016, WIAS Berlin, May 11, 2016.

  • S.P. Frigeri, On some nonlocal diffuse-interface models for binary fluids: Regularity results and applications, Congress of the Italian Society of Industrial and Applied Mathematics (SIMAI 2016), September 13 - 16, 2016, Politecnico di Milano, Italy, September 14, 2016.

  • S.P. Frigeri, Optimal distributed control for nonlocal Cahn--Hilliard/Navier--Stokes systems in 2D, International INdAM Conference ``Optimal Control for Evolutionary PDEs and Related Topics (OCERTO 2016)'', June 20 - 24, 2016, Cortona, Italy, June 24, 2016.

  • R. Henrion, Aspects of nondifferentiability for probability functions, 7th International Seminar on Optimization and Variational Analysis, June 1 - 3, 2016, Universidad de Alicante, Spain, June 2, 2016.

  • R. Henrion, Aspects of nonsmoothness for Gaussian probability functions, PGMO Days 2016 -- Gaspard Monge Program for Optimization and Operations Research, November 8 - 9, 2016, Electricité de France, Palaiseau, France, November 9, 2016.

  • R. Henrion, Calmness of the perturbation mappings for MPECs in original and enhanced form, International Conference on Bilevel Optimization and Related Topics, May 4 - 6, 2016, Dresden, May 6, 2016.

  • M. Hintermüller, S. Hajian, N. Strogies, Subproject B02 -- Parameter id., sensor localization and quantification of uncertainties in switched PDE systems, Annual Meeting of the Collaborative Research Center/Transregio (TRR) 154 ``Mathematical Modeling, Simulation and Optimization Using the Example of Gas Networks'', Technische Universität Berlin, October 4 - 5, 2016.

  • M. Hintermüller, S. Hajian, N. Strogies, Subproject B02 -- Parameter id., sensor localization and quantification of uncertainties in switched PDE systems, Conference ``Mathematics of Gas Transport'', Konrad-Zuse-Zentrum für Informationstechnik Berlin, October 6 - 7, 2016.

  • M. Hintermüller, Adaptive finite elements in total variation based image denoising, SIAM Conference on Imaging Science, Minisymposium ``Leveraging Ideas from Imaging Science in PDE-constrained Optimization'', May 23 - 26, 2016, Albuquerque, USA, May 24, 2016.

  • M. Hintermüller, Bilevel optimization for a generalized total-variation model, SIAM Conference on Imaging Science, Minisymposium ``Non-Convex Regularization Methods in Image Restoration'', May 23 - 26, 2016, Albuquerque, USA, May 26, 2016.

  • M. Hintermüller, Nonsmooth structures in PDE constrained optimization, 66th Workshop ``Advances in Convex Analysis and Optimization'', July 5 - 10, 2016, International Centre for Scientific Culture ``E. Majorana'', School of Mathematics ``G. Stampacchia'', Erice, Italy, July 9, 2016.

  • M. Hintermüller, Optimal control of multiphase fluids and droplets, WIAS-PGMO Workshop on Nonsmooth and Stochastic Optimization with Applications to Energy Management, May 10 - 12, 2016, WIAS Berlin, May 11, 2016.

  • M. Hintermüller, Optimal control of multiphase fluids and droplets, The Fifth International Conference on Continuous Optimization, Session: ``Recent Developments in PDE-constrained Optimization I'', August 6 - 11, 2016, Tokyo, Japan, August 10, 2016.

  • M. Hintermüller, Optimal control of multiphase fluids and droplets, Salzburg Mathematics Colloquium, Universität Salzburg, Fachbereich Mathematik, Austria, June 9, 2016.

  • M. Hintermüller, Optimal selection of the regularisation function in a localised TV model, SIAM Conference on Imaging Science, Minisymposium ``Analysis and Parameterisation of Derivative Based Regularisation'', May 23 - 26, 2016, Albuquerque, USA, May 24, 2016.

  • M. Hintermüller, Recent trends in optimal control problems with nonsmooth structures, Computational Methods for Control of Infinite-dimensional Systems, March 14 - 18, 2016, Institute for Mathematics and its Applications, Minneapolis, USA, March 14, 2016.

  • M. Hintermüller, Towards sharp stationarity conditions for classes of optimal control problems for variational inequalities of the second kind, International INdAM Conference ``Optimal Control for Evolutionary PDEs and Related Topics (OCERTO 2016)'', June 20 - 24, 2016, Cortona, Italy, June 20, 2016.

  • D. Hömberg, Analysis and simulation of Joule heating problems, Mathematisches Kolloquium, Bergische Universität Wuppertal, Fachgruppe Mathematik und Informatik, June 21, 2016.

  • D. Hömberg, Math for steel production and manufacturing, MACSI10 -- Empowering Industrial Mathematical and Statistical Modelling for the Future, December 8 - 9, 2016, University of Limerick, Ireland, December 9, 2016.

  • M. Eigel, Reliable averaging for the primal variable in the courant FEM and hierarchical error estimators on red-refined meshes, 28th Chemnitz FEM Symposium 2015, September 28 - 30, 2015, Burgstädt, September 29, 2015.

  • CH. Heinemann, Solvability of differential inclusions describing damage processes and applications to optimal control problems, Universität Essen-Duisburg, Fakultät für Mathematik, Essen, December 3, 2015.

  • D. Peschka, Mathematical modeling, analysis, and optimization of strained germanium-microbridges, sc Matheon Center Days, April 20 - 21, 2015, Technische Universität Berlin, Institut für Mathematik, Berlin, April 20, 2015.

  • J. Sprekels, Optimal boundary control problems for Cahn--Hilliard systems with dynamic boundary conditions, INdAM Workshop ``Special Materials in Complex Systems -- SMaCS 2015'', May 18 - 22, 2015, Rome, Italy, May 21, 2015.

  • M.H. Farshbaf Shaker, A deep quench approach to the optimal control of an Allen--Cahn equation with dynamic boundary conditions, National Institute for Mathematical Sciences, Division of Computational Mathematics, Daejeon, Korea (Republic of), May 20, 2015.

  • M.H. Farshbaf Shaker, Introduction into optimal control of partial differential equations, May 14 - 18, 2015, National Institute for Mathematical Sciences, Division of Computational Mathematics, Daejeon, Korea (Republic of).

  • M.H. Farshbaf Shaker, Multi-material phase field approach to structural topology optimization and its relation to sharp interface approach, University of Tokyo, Graduate School of Mathematical Sciences, Japan, October 6, 2015.

  • M.H. Farshbaf Shaker, Relating phase field and sharp interface approaches to structural topology optimization, National Institute for Mathematical Sciences, Division of Computational Mathematics, Daejeon, Korea (Republic of), May 13, 2015.

  • M.H. Farshbaf Shaker, Relating phase field and sharp interface approaches to structural topology optimization, Technische Universität Berlin, Institut für Mathematik, February 5, 2015.

  • CH. Heinemann, Well-posedness of strong solutions for a damage model in 2D, Universitá di Brescia, Department DICATAM -- Section of Mathematics, Italy, March 13, 2015.

  • R. Henrion, (Sub-) Gradient formulae for probability functions with Gaussian distribution, PGMO Days 2015 -- Gaspard Monge Program for Optimization and Operations Research, October 27 - 28, 2015, ENSTA ParisTech, Palaiseau, France, October 28, 2015.

  • R. Henrion, (Sub-)Gradient formulae for probability functions with applications to power management, Universidad de Chile, Centro de Modelamiento Matemático, Santiago de Chile, Chile, November 25, 2015.

  • R. Henrion, Calmness as a constraint qualification for MPECs, International Conference on Variational Analysis, Optimization and Quantitative Finance in Honor of Terry Rockafellar's 80th Birthday, May 18 - 22, 2015, Université de Limoges, France, May 21, 2015.

  • R. Henrion, Conditioning of linear-quadratic two-stage stochastic optimization problems, Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic, March 26, 2015.

  • R. Henrion, On some relations between probability functions and variational analysis, International Workshop ``Variational Analysis and Applications'', August 28 - September 5, 2015, Erice, Italy, August 31, 2015.

  • D. Hömberg, A crash course on optimal control, Fudan University, School of Mathematical Sciences, Shanghai, China, March 18, 2015.

  • D. Hömberg, Nucleation, growth, and grain size evolution in multiphase materials, INdAM Workshop ``Special Materials in Complex Systems -- SMaCS 2015'', May 18 - 22, 2015, Rome, Italy, May 21, 2015.

  • D. Hömberg, Optimal coefficient control for semilinear parabolic equations, Fudan University, School of Mathematical Sciences, Shanghai, China, March 10, 2015.

  • D. Hömberg, The digital factory -- A perspective for a closer cooperation between math and industry, Workshop ``Mathematics and Computer Science in Practice: Potential and Reality'', December 9 - 11, 2015, Prague, Czech Republic, December 9, 2015.

  • J. Sprekels, Optimal boundary control problems for Cahn--Hilliard systems with singular potentials and dynamic boundary conditions, Romanian Academy, Simeon Stoilow Institute of Mathematics, Bucharest, March 18, 2015.

  • N. Togobytska, Optimal control approach for production of multiphase steels, The 18th European Conference on Mathematics for Industry 2014 (ECMI 2014), Minisymposium 37: Simulation and Control of Hot-rolling, June 9 - 13, 2014, Taormina, Italy, June 9, 2014.

  • M. Eigel, Guaranteed a posteriori error control with adaptive stochastic Galerkin FEM, SIAM Conference on Uncertainty Quantification (UQ14), March 31 - April 3, 2014, Savannah, USA, April 1, 2014.

  • TH. Petzold, Modellierung, Simulation und Optimierung in angewandter Mathematik am Weierstraß-Institut, Innovation Days 2014, December 1 - 2, 2014, München, December 2, 2014.

  • K. Sturm, Optimal control and shape design problems in thermomechanics, BMS-WIAS Summer School ``Applied Analysis for Materials'', August 25 - September 5, 2014, Berlin Mathematical School, Technische Universität Berlin, September 2, 2014.

  • M.H. Farshbaf Shaker, A deep quench approach to the optimal control of an Allen--Cahn equation with dynamic boundary conditions and double obstacles, Conference on Partial Differential Equations, May 28 - 31, 2014, Novacella, Italy, May 29, 2014.

  • M.H. Farshbaf Shaker, Relating phase field and sharp interface approaches to structural topology optimization, SADCO-WIAS Young Researcher Workshop, January 29 - 31, 2014, WIAS, January 31, 2014.

  • R. Henrion, Calmness as a constraint qualification for MPECs, German Polish Conference on Optimization Methods and Applications, February 28 - March 4, 2014, Wittenberg, March 1, 2014.

  • R. Henrion, Calmness as a constraint qualification for MPECs, 6th Seminar on Optimization and Variational Analysis, University of Elche, Spain, June 3, 2014.

  • R. Henrion, Conditioning of linear-quadratic two-stage stochastic optimization problems, 5th Conference on Optimization Theory and its Applications (ALEL 2014), June 5 - 7, 2014, Universidad de Sevilla, Spain, June 6, 2014.

  • R. Henrion, Nichtlineare Optimierung bei unsicheren Nebenbedingungen, 1. Arbeitstreffen zur Initiative ``Biokybernetik'', November 20 - 21, 2014, Großkarlbach, November 20, 2014.

  • D. Hömberg, Modelling and simulation of multi-frequency induction hardening, Ecole Polytechnique, Laboratoire de Mécanique des Solides, Palaiseau, France, March 13, 2014.

  • D. Hömberg, Modelling, analysis and simulation of multifrequency induction hardening, Norwegian University of Science and Technology, Department of Mathematical Sciences, Trondheim, October 21, 2014.

  • D. Hömberg, Modelling, simulation and control of surface heat treatments, Norwegian University of Science and Technology, Department of Physics, Trondheim, October 31, 2014.

  • D. Hömberg, Multifrequency induction hardening --- Modelling, analysis, and simulation, Fudan University, School of Mathematical Sciences, Shanghai, China, March 4, 2014.

  • D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, Workshop ``Recent Developments and Challenges in Interface and Free Boundary Problems'', March 25 - 28, 2014, University of Warwick, UK, March 26, 2014.

  • D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, The 18th European Conference on Mathematics for Industry 2014 (ECMI 2014), Minisymposium 37: Simulation and Control of Hot-rolling, June 9 - 13, 2014, Taormina, Italy, June 9, 2014.

  • D. Hömberg, Nucleation, growth, and grain size evolution in dual phase steels, Wrocław University of Technology, Institute of Mathematics and Computer Science, Poland, July 1, 2014.

  • D. Hömberg, Oberflächenbearbeitung mit Mathematik, Opel Innovation Day, Rüsselsheim, November 7, 2014.

  • D. Hömberg, Optimal control and shape design problems in thermomechanics, BMS-WIAS Summer School ``Applied Analysis for Materials'', August 25 - September 5, 2014, Berlin Mathematical School, Technische Universität Berlin, September 1, 2014.

  • J. Sprekels, Introduction into the optimal control of PDEs, SADCO-WIAS Young Researcher Workshop, January 29 - 31, 2014, WIAS, January 31, 2014.

  • CH. Landry, Collision detection between robots moving along specified paths, Universität der Bundeswehr München, Institut für Mathematik und Rechneranwendung, Neubiberg, May 15, 2013.

  • CH. Landry, Optimizing work cells in automotive industry, Mathematics for Industry and Society, July 4 - 5, 2013, French Embassy, Berlin, July 5, 2013.

  • CH. Landry, Task assignment, sequencing and path-planning in robotic welding cells, 18th International Conference on Methods and Models in Automation and Robotics, August 26 - 29, 2013, Miedzyzdroje, Poland, August 27, 2013.

  • M. Eigel, Advances in adaptive stochastic Galerkin FEM, Workshop ``Partial Differential Equations with Random Coefficients'', November 13 - 15, 2013, WIAS, Berlin, November 14, 2013.

  • M. Eigel, On tensor approximations with adaptive stochastic Galerkin FEM, Eidgenössische Technische Hochschule Zürich, Seminar für Angewandte Mathematik, Switzerland, September 25, 2013.

  • M.H. Farshbaf Shaker, Relating phase field and sharp interface approaches to structural topology optimization, The Fourth International Conference on Continuous Optimization (ICCOPT), July 27 - August 1, 2013, Universidade Nova de Lisboa, Lisbon, Portugal, July 31, 2013.

  • R. Henrion, Dual stationarity conditions for MPECs, CIMPA-UNESCO-MESR-MINECO-INDIA Research School ``Generalized Nash Equilibrium Problems, Bilevel Programming and MPES'', November 25 - December 6, 2013, University of Delhi, India.

  • R. Henrion, Optimierungsprobleme mit Wahrscheinlichkeitsrestriktionen, Technische Universität Darmstadt, Fachbereich Mathematik, September 16, 2013.

  • R. Henrion, Optimization problems with probabilistic constraints, Workshop ``Numerical Methods for PDE Constrained Optimization with Uncertain Data'', January 27 - February 2, 2013, Mathematisches Forschungsinstitut Oberwolfach, January 30, 2013.

  • R. Henrion, Optimization problems with probabilistic constraints, Universität Göttingen, Institut für Numerische und Angewandte Mathematik, January 8, 2013.

  • R. Henrion, Optimization problems with probabilistic constraints, March 19 - 21, 2013, University of Ostrava, Department of Mathematics, Czech Republic.

  • R. Henrion, Problèmes d'optimisation avec des contraintes en probabilité, Electricité de France, Clamart, France, June 20, 2013.

  • R. Henrion, Stochastic optimization with probabilistic constraints, International Conference on Stochastic Programming (SP XIII), July 8 - 12, 2013, Bergamo, Italy, July 9, 2013.

  • R. Henrion, Optimisation sous contraintes en probabilité, Journées annuelles 2013 du Groupe de Recherche MOA, June 17 - 19, 2013, Paris, France, June 17, 2013.

  • D. Hömberg, An optimal shape design approach towards distortion compensation, Equadiff13, MS21 -- Recent Trends in PDE-constrained Control and Shape Design, August 26 - 30, 2013, Prague, Czech Republic, August 29, 2013.

  • D. Hömberg, An optimal shape design approach towards distortion compensation, Fudan University, School of Mathematics, Shanghai, China, March 6, 2013.

  • D. Hömberg, Mathematics for the digital factory, Mathematics for Industry and Society, July 4 - 5, 2013, French Embassy, Berlin, July 5, 2013.

  • D. Hömberg, MeFreSim --- Modellierung, Simulation und Optimierung des Mehrfrequenzverfahrens für die induktive Wärmebehandlung als Bestandteil der modernen Fertigung, BMBF Status Seminar ``Mathematik für Innovationen in Industrie und Dienstleistung'', June 20 - 21, 2013, Bonn, June 21, 2013.

  • D. Hömberg, Modelling, analysis and simulation of multifrequency induction hardening, Forum Math-for-Industry 2013 ``The Impact of Applications on Mathematics'', November 4 - 8, 2013, Kyushu University, Fukuoka, Japan, November 7, 2013.

  • D. Hömberg, On a phase field approach to shape optimization, Université de Paris-Sud, Laboratoire de Mathématiques, Equipe Analyse Numérique et EDP, France, January 16, 2013.

  • D. Hömberg, Sufficient optimality conditions for a semi-linear parabolic system, University of Tokyo, Graduate School of Mathematical Sciences, Japan, February 27, 2013.

  • J. Sprekels, Optimal control of Allen--Cahn equations with singular potentials and dynamic boundary conditions, DIMO2013 -- Diffuse Interface Models, September 10 - 13, 2013, Levico Terme, Italy, September 11, 2013.

  • J. Sprekels, Optimal control of the Allen--Cahn equation with dynamic boundary condition and double obstacle potentials: A ``deep quench'' approach, Applied Mathematics Seminar, Università di Pavia, Dipartimento di Matematica ``F. Casorati'', Italy, September 17, 2013.

  • CH. Landry, An optimal control problem for the collision-free motion planning of industrial robots, École Polytechnique Fédérale de Lausanne, Mathematics Institute of Computational Science and Engineering (MATHICSE), Switzerland, November 28, 2012.

  • CH. Landry, Collision-free path planning of welding robots, The 17th European Conference on Mathematics for Industry 2012 (ECMI 2012), July 23 - 27, 2012, Lund, Sweden, July 24, 2012.

  • CH. Landry, Modeling of the optimal trajectory of industrial robots in the presence of obstacles, 21st International Symposium on Mathematical Programming (ISMP), August 19 - 24, 2012, Technische Universität Berlin, August 19, 20122012.

  • K. Sturm, Shape optimization for an interface problem in linear elasticity for distortion compensation, 21st International Symposium on Mathematical Programming (ISMP), August 19 - 24, 2012, Technische Universität Berlin, August 20, 2012.

  • R. Henrion, On (co-)derivatives of the solution map to a class of generalized equations, 21st International Symposium on Mathematical Programming (ISMP), August 19 - 24, 2012, Technische Universität Berlin, August 23, 2012.

  • R. Henrion, On the coderivative of normal cone mappings to moving sets, 58th Course ``Variational Analysis and Applications'', May 14 - 22, 2012, International School of Mathematics ``Guido Stampacchia'', Erice, Italy, May 18, 2012.

  • D. Hömberg, On a phase field approach to topology optimization, Mini-Workshop ``Geometries, Shapes and Topologies in PDE-based Applications'', November 25 - December 1, 2012, Mathematisches Forschungsinstitut Oberwolfach, November 27, 2012.

  • D. Hömberg, On the phase field approach to shape and topology optimization, University of Tokyo, Graduate School of Mathematical Sciences, Japan, March 6, 2012.

  • D. Hömberg, Optimal control of multifrequency induction hardening, INDAM Workshop PDEs for Multiphase Advanced Materials (ADMAT2012), September 17 - 21, 2012, Cortona, Italy, September 18, 2012.

  • D. Hömberg, Optimal control of multiphase steel production, 21st International Symposium on Mathematical Programming (ISMP), July 21, 19 - August 24, 2012, Technische Universität Berlin, August 23, 2012.

  • J. Sprekels, A time discretization for a nonstandard viscous Cahn--Hilliard system, INDAM Workshop PDEs for Multiphase Advanced Materials (ADMAT2012), September 17 - 21, 2012, Cortona, Italy, September 19, 2012.

  • J. Sprekels, Optimal control problems arising in the industrial growth of bulk semiconductor single crystals, 21st International Symposium on Mathematical Programming (ISMP), Invited Session ``Optimization Applications in Industry I'', August 19 - 24, 2012, Technische Universität Berlin, August 21, 2012.

  • J. Sprekels, Optimal control problems arising in the industrial growth of bulk single semiconductor crystals, Applied Mathematics Seminar, Università di Pavia, Dipartimento di Matematica ``F. Casorati'', Italy, September 11, 2012.

  • CH. Landry, A minimum time control problem for finding robot motion planning, Optimization 2011, July 24 - 27, 2011, Lisbon, Portugal, July 25, 2011.

  • TH. Arnold, On Born approximation for the scattering by rough surfaces, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12 - 16, 2011, Technische Universität Berlin, September 15, 2011.

  • A. Möller, Capacity planning in energy networks by probabilistic programming, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12 - 16, 2011, Technische Universität Berlin, September 14, 2011.

  • R. Henrion, Progress and challenges in chance-constrained programming, SIGOPT --- International Conference on Optimization 2011, June 15 - 17, 2011, Pfalz-Akademie Lambrecht, June 15, 2011.

  • D. Hömberg, Mathematical concepts in steel manufacturing, Fudan University, School of Mathematics, Shanghai, China, March 29, 2011.

  • D. Hömberg, Optimal boundary coefficient control for parabolic equations, Interfaces and Discontinuities in Solids, Liquids and Crystals (INDI2011), June 20 - 23, 2011, Gargnano (Brescia), Italy, June 20, 2011.

  • D. Hömberg, Optimal control problems in thermomechanics, Schwerpunktskolloquium ``Analysis und Numerik'', Universität Konstanz, Fachbereich Mathematik und Statistik, January 20, 2011.

  • D. Hömberg, Solid-solid phase transitions: From surface hardening of steel to laser thermo-therapy, Southeast University, Department of Mathematics, Nanjing, China, March 28, 2011.

  • J. Sprekels, A non-standard phase-field system of Cahn--Hilliard type for diffusive phase segregation, Schwerpunktkolloquium``Analysis und Numerik'', Universität Konstanz, Fachbereich Mathematik und Statistik, July 14, 2011.

  • J. Sprekels, A nonstandard phase field system of Cahn--Hilliard type for diffusive phase segregation, Seminario Matematico e Fisico di Milano, Università degli Studi di Milano, Dipartimento di Matematica, Italy, September 21, 2011.

  • R. Henrion, On calmness conditions in convex bilevel programming, SIAM Conference on Optimization, May 16 - 19, 2011, Darmstadt, May 16, 2011.

  • R. Henrion, On joint linear probabilistic constraints with Gaussian coefficient matrix, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12 - 16, 2011, Technische Universität Berlin, September 14, 2011.

  • R. Henrion, Structure, stability and algorithmic issues of optimization problems with probabilistic constraints, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12 - 16, 2011, Technische Universität Berlin, September 16, 2011.

  • D. Hömberg, Modelling, simulation and control of multiphase steel production, International Congress on Modelling and Simulation (MODSIM 2011), December 12 - 16, 2011, Perth, Australia, December 15, 2011.

  • D. Hömberg, On the phase field approach to shape and topology optimization, Università degli Studi di Pavia, Dipartimento di Matematica ``F. Casorati'', Italy, November 15, 2011.

  • K. Krumbiegel, Optimal control approach for production of modern multiphase steels, International Congress on Industrial and Applied Mathematics (ICIAM), July 18 - 22, 2011, Vancouver, Canada, July 18, 2011.

  • K. Krumbiegel, Superconvergence properties for semilinear elliptic boundary control problems, 25th IFIP TC 7 Conference on System Modeling and Optimization, September 12 - 16, 2011, Technische Universität Berlin, September 15, 2011.

  • J. Sprekels, Well-posedness, asymptotic behavior and optimal control of a nonstandard phase field model for diffusive phase segregation, Workshop on Optimal Control of Partial Differential Equations, November 28 - December 1, 2011, Wasserschloss Klaffenbach, Chemnitz, November 30, 2011.

  • N. Togobytska, An inverse problem for laser-induced thermotherapy arising in tumor tissue imaging, Chemnitz Symposium on Inverse Problems 2010, September 23 - 24, 2010, September 24, 2010.

  • R. Henrion, Chance-constrained problems, Pre-Conference PhD Workshop, 12th Conference on Stochastic Programming (SPXII), Halifax, Canada, August 15, 2010.

  • R. Henrion, On a dynamic model for chance constrained programming, 12th Conference on Stochastic Programming (SPXII), August 16 - 20, 2010, Halifax, Canada, August 17, 2010.

  • R. Henrion, Optimization problems with probabilistic constraints, 3rd International Conference on Continuous Optimization (ICCOPT), July 26 - 29, 2010, Santiago de Chile, July 27, 2010.

  • D. Hömberg, A brief introduction to PDE-constrained control, Warsaw Seminar on Industrial Mathematics (WSIM'10), March 18 - 19, 2010, Warsaw University of Technology, Poland, March 18, 2010.

  • D. Hömberg, Steel manufacturing --- A challenge for applied mathematics, Universität Duisburg-Essen, Fachbereich Mathematik, May 11, 2010.

  • D. Hömberg, The mathematics of distortion, ``Seminario Matematico e Fisico di Milano'', Università degli Studi di Milano, Dipartimento di Matematica, Italy, March 1, 2010.

  • K. Krumbiegel, Numerical analysis for elliptic Neumann boundary control problems with pointwise state and control constraints, Technische Universität Dresden, Institut für Numerische Mathematik, May 11, 2010.

  • K. Krumbiegel, On the convergence and second order sufficient optimality conditions of the virtual control concept for semilinear state constrained optimal control problems, Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria, May 18, 2010.

  • K. Krumbiegel, On the convergence and second order sufficient optimality conditions of the virtual control concept for semilinear state constrained optimal control problems, Summer School ``Optimal Control of Partial Differential Equations'', July 12 - 17, 2010, Cortona, Italy, July 16, 2010.

  • K. Krumbiegel, Sufficient optimality conditions for the Moreau--Yosida type regularization concept applied to state constrained problems, Gemeinsame Jahrestagung Deutsche Mathematiker-Vereinigung (DMV) und Gesellschaft für Didaktik der Mathematik (GDM), March 8 - 12, 2010, Ludwig-Maximilians-Universität München, March 10, 2010.

  • K. Krumbiegel, Sufficient optimality conditions for the Moreau-Yosida type regularization concept applied to state constrained problems, 81th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2010), March 22 - 26, 2010, Universität Karlsruhe, March 25, 2010.

  • J. Sprekels, Introduction to Optimal Control Problems for PDEs (mini-course), Summer School ``Optimal Control of Partial Differential Equations'', July 12 - 17, 2010, Cortona, Italy.

  • R. Henrion, A model for dynamic chance constraints in water reservoir management, 23rd European Conference on Operational Research (EURO23), July 6 - 8, 2009, Bonn, July 7, 2009.

  • R. Henrion, Answers and questions in selected topics of probabilistic programming, International Colloquium on Stochastic Modeling and Optimization, November 30 - December 1, 2009, Rutgers University, New Brunswick, USA, November 30, 2009.

  • R. Henrion, On stationarity conditions for an equilibrium problem with equilibrium constraints from an electricity spot market model, 23rd European Conference on Operational Research (EURO23), July 6 - 8, 2009, Bonn, July 7, 2009.

  • D. Hömberg, Die Wärmebehandlung von Stahl --- Thermomechanische Modellierung, Simulation und Optimierung, Technische Universität Dortmund, Fakultät Maschinenbau, January 22, 2009.

  • D. Hömberg, Direct and inverse problems related to phase transitions and distortion in modern multi-phase steels, Workshop ``Mathematical Models and Analytical Problems for Special Materials'', July 9 - 11, 2009, Università degli Studi di Brescia, Italy, July 9, 2009.

  • D. Hömberg, Distortion compensation --- An optimal control approach, 24th IFIP TC 7 Conference on System Modelling and Optimization, July 27 - 31, 2009, Buenos Aires, Argentina, July 27, 2009.

  • D. Hömberg, Optimal control of heat treatments and stability of milling processes --- Two case studies from industrial mathematics, Worcester Polytechnic Institute, Mechanical Engineering Department, USA, October 7, 2009.

  • D. Hömberg, The mathematics of distortion, University of Delaware, Department of Mathematical Sciences, Newark, USA, October 6, 2009.

  • K. Krumbiegel, Optimalsteuerung mit Zustandsbeschränkungen, Universität Leipzig, Fakultät für Mathematik und Informatik, October 6, 2009.

  • W. Bleck, D. Hömberg, Ch. Keul, U. Prahl, P. Suwanpinij, N. Togobytska, Simulation, Optimierung und Regelung von Gefügebildung und mechanischen Eigenschaften beim Warmwalzen von Mehrphasenstählen, Workshop ``MEFORM 2008: Simulation von Umformprozessen'', Freiberg, March 26 - 28, 2008.

  • R. Henrion, Distance to uncontrollability for convex processes, SIGOPT International Conference on Optimization, February 18 - 21, 2008, Lambrecht, February 19, 2008.

  • R. Henrion, On a dynamical model for chance constrained programming, Conference on Optimization & Practices in Industry (COPI08), November 26 - 28, 2008, Clamart, France, November 28, 2008.

  • R. Henrion, On calculating the normal cone to a finite union of convex polyhedra, World Congress of Nonlinear Analysts (WCNA 2008), July 2 - 9, 2008, Orlando, USA, July 3, 2008.

  • D. Hömberg, Modellierung und Optimierung der Gefügeumwandlung in niedrig legierten Stählen und Anwendungen, Salzgitter Mannesmann Forschung GmbH, February 19, 2008.

  • D. Hömberg, Prozesskette Stahl, Workshop of scshape Matheon with Siemens AG (Industry Sector) in cooperation with Center of Knowledge Interchange (CKI) of Technische Universität (TU) Berlin and Siemens AG, TU Berlin, September 29, 2008.

  • D. Hömberg, Solid-solid phase transitions --- Analysis, optimal control and industrial application, Warsaw University of Technology, Faculty of Mathematics and Information Science, Poland, February 14, 2008.

  • D. Hömberg, The heat treatment of steel --- A mathematical control problem, 2nd International Conference on Distortion Engineering 2008, September 17 - 19, 2008, Bremen, September 19, 2008.

  • R. Henrion, Avoidance of random obstacles by means of probabilistic constraints, 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), July 16 - 20, 2007, ETH Zürich, Switzerland, July 16, 2007.

  • R. Henrion, Chance-constrained stochastic programming, Spring School on Stochastic Programming: Theory and Applications, University of Bergamo, Italy, April 12, 2007.

  • R. Henrion, Contraintes en probabilité: synthèse bibliographique et approche à la situation dynamique, Electricité de France R&D, Clamart, France, November 28, 2007.

  • R. Henrion, Distance to uncontrollability for convex processes, International Congress ``Mathematical Methods in Economics and Industry'' (MMEI 2007), June 3--7, Herlany, Slovakia, June 5, 2007.

  • R. Henrion, Eventual convexity and related properties of probabilistic constraints, 11th Conference on Stochastic Programming (SPXI), August 27 - 31, 2007, Vienna, Austria, August 31, 2007.

  • D. Hömberg, D. Kern, Optimal control of a thermomechanical model of phase transitions in steel, 6th International Congress on Industrial and Applied Mathematics (ICIAM 2007), July 16 - 20, 2007, ETH Zürich, Switzerland, July 19, 2007.

  • D. Hömberg, A short course on PDE-constrained optimal control, March 20 - 30, 2007, Universitá degli Studi di Milano, Dipartimento di Matematica, Italy.

  • D. Hömberg, Mathematical tools for the simulation and control of heat treatments, Delphi, Puerto Real, Spain, January 16, 2007.

  • D. Hömberg, Mathematics for steel production and manufacturing, Nippon Steel, Kimitsu, Japan, March 1, 2007.

  • D. Hömberg, On a thermomechanical phase transition model for the heat treatment of steel, Universidad de Cádiz, Departamento de Matemáticas, Puerto Real, Spain, January 15, 2007.

  • D. Hömberg, On a thermomechanical phase transition model for the heat treatment of steel, Fudan University, Department of Mathematics, Shanghai, China, March 5, 2007.

  • D. Hömberg, Optimal control of semilinear parabolic equations and an application to laser material treatments (part I), University of Tokyo, Department of Mathematical Sciences, Japan, February 21, 2007.

  • D. Hömberg, Optimal control of semilinear parabolic equations and an application to laser material treatments (part II), University of Tokyo, Department of Mathematical Sciences, Japan, February 22, 2007.

  • D. Hömberg, Thermomechanical phase transition models --- analysis, optimal control and industrial applications, University of Oxford, Oxford Centre for Industrial and Applied Mathematics, UK, October 11, 2007.

  • R. Henrion, Initiation aux contraintes en probabilité, Electricité de France R&D, Clamart, France, May 17, 2006.

  • R. Henrion, On chance constraints with random coefficient matrix, 19th International Symposium on Mathematical Programming (ISMP 2006), Rio de Janeiro, Brazil, August 3, 2006.

  • R. Henrion, Quelques propriétés structurelles de contraintes en probabilité, Ecole Nationale des Ponts et Chaussées, Marne-la-Vallée, France, May 16, 2006.

  • R. Henrion, Structural analysis for some basic types of probabilistic constraints, Prague Stochastics 2006, Czech Republic, August 25, 2006.

  • D. Hömberg, A crash course in Nonlinear Optimization, November 13 - 23, 2006, Escuela Politécnica Nacional, Quito, Ecuador.

  • D. Hömberg, Die Wärmebehandlung von Stahl --- ein Optimierungsproblem, Universität Bremen, SFB 570 ``Distortion Engineering'', March 2, 2006.

  • D. Hömberg, Laser surface hardening --- modelling, simulation and optimal control, 4th Korean-German Seminar on Applied Mathematics and Physics, September 24 - October 1, 2006, Erlangen, September 26, 2006.

  • D. Hömberg, Modellierung, Simulation und Optimierung der Wärmebehandlung von Stahl, Endress+Hauser Flowtec AG, Reinach, Switzerland, May 15, 2006.

  • D. Hömberg, Optimal control of a thermomechanical phase transition model, 12th IEEE International Conference on Methods and Models in Automation and Robotics, August 28 - 31, 2006, Miedzyzdroje, Poland, August 29, 2006.

  • D. Hömberg, Optimal control of laser material treatments, 21st European Conference on Operational Research (EURO XXI), July 3 - 5, 2006, Reykjavik, Iceland, July 3, 2006.

  • D. Hömberg, Optimal control of thermomechanical phase transitions, Workshop ``Inverse and Control Problems for PDE's'', March 13 - 17, 2006, Rome, Italy, March 13, 2006.

  • D. Hömberg, Phasenübergänge in Stahl, Summer School ``Simulation und Anwendungen von Mikrostrukturen'', August 14 - 18, 2006, Föhr.

  • D. Hömberg, Thermomechanical models of phase transitions --- modelling, control and industrial applications, Escuela Politécnica Nacional, Departamento de Matématica, Quito, Ecuador, November 13, 2006.

  • R. Henrion, T. Szántai, Properties and calculation of singular normal distributions, Dagstuhl Seminar on ``Algorithms for Optimization with Incomplete Information'', Schloss Dagstuhl, January 17, 2005.

  • R. Henrion, Calmness of chance constraints and Lipschitz properties of the value-at-risk, 22nd IFIP TC 7 Conference on System Modeling and Optimization, July 18 - 22, 2005, Turin, Italy, July 21, 2005.

  • R. Henrion, On the structure of linear chance constraints with random coefficients, Conference on Optimization under Uncertainties (COUCH 2005), September 28 - 30, 2005, Heidelberg, September 29, 2005.

  • R. Henrion, Properties of linear probabilistic constraints, INFORMS Annual Meeting, November 13 - 16, 2005, San Francisco, USA, November 14, 2005.

  • R. Henrion, Stability of solutions in programs with probabilistic constraints, 10-th Workshop on Well-posedness of Optimization Problems and Related Topics, September 5 - 9, 2005, Borovets, Bulgaria, September 9, 2005.

  • D. Hömberg, A thermomechanical phase transition model for the surface hardening of steel, International Conference ``Free Boundary Problems: Theory and Applications'', June 7 - 12, 2005, Coimbra, Portugal, June 11, 2005.

  • D. Hömberg, Control of laser material treatments, SIAM Conference on Mathematics for Industry, October 24 - 26, 2005, Detroit Marriott Renaissance Center, USA, October 25, 2005.

  • D. Hömberg, Die Laserhärtung von Stahl --- Modellierung, Analysis und optimale Steuerung, Universität Bayreuth, Mathematisches Institut, June 30, 2005.

  • D. Hömberg, Laser material treatments --- modeling, simulation, and optimal control, Michigan State University, Department of Mathematics, East Lansing, USA, October 27, 2005.

  • D. Hömberg, Modelling, simulation and control of laser material treatments, Scuola Normale Superiore, Pisa, Italy, November 22, 2005.

  • D. Hömberg, On a thermomechanical model of surface heat treatments, EQUADIFF 11 International conference on differential equations, July 25 - 29, 2005, Comenius University, Bratislava, Slovakia, July 28, 2005.

  • D. Hömberg, Optimal control of solid-solid phase transitions including mechanical effects, Workshop ``Optimal Control of Coupled Systems of PDE'', April 17 - 23, 2005, Mathematisches Forschungsinstitut Oberwolfach, April 22, 2005.

  • D. Hömberg, Von der Stahlhärtung bis zur Krebstherapie --- Simulations- und Optimierungsaufgaben in Lehre und Forschung, FEMLAB Konferenz 2005, November 3 - 4, 2005, Frankfurt am Main, November 3, 2005.

  • R. Henrion, J. Outrata, Calmness of constraint systems with applications, French-German-Spanish Conference on Optimization, September 20 - 24, 2004, University of Avignon, France, September 21, 2004.

  • R. Henrion, (Sub-)Differentiability and Lipschitz properties of singular normal distributions, 10th International Conference on Stochastic Programming, October 8 - 15, 2004, University of Arizona, Tucson, USA, October 15, 2004.

  • R. Henrion, Optimization problems with probabilistic constraints, 10th International Conference on Stochastic Programming, October 8 - 15, 2004, University of Arizona, Tucson, USA, October 9, 2004.

  • R. Henrion, Selected aspects of structure, stability and numerics in chance-constrained optimization problems, Workshop on Optimization of Stochastic Systems, Stevens Institute of Technology, Hoboken, USA, April 30, 2004.

  • R. Henrion, Some results on stability, structure and numerics in programs with probabilistic constraints, Universität Zürich, Wirtschaftswissenschaftliche Fakultät, Switzerland, December 20, 2004.

  • R. Henrion, Sur des applications multivôques du type 'calme', Séminaire de l'Equipe ACSIOM (Analyse, Calcul Scientifique Industriel et Optimisation de Montpellier), Université Montpellier, France, November 16, 2004.

  • D. Hömberg, Modellierung, Analysis und optimale Steuerung der Lasermaterialbearbeitung, Kolloquium der Angewandten Mathematik, Universität Münster, December 3, 2004.

  • D. Hömberg, Optimal control of laser surface hardening, University of Chiba, Department of Mathematics and Informatics, Japan, October 19, 2004.

  • D. Hömberg, Simulation und Optimierung der Lasermaterialbearbeitung, Seminar des Forschungsschwerpunktes Photonik, Technische Universität Berlin, Optisches Institut, June 18, 2004.

  • D. Hömberg, The induction hardening of steel --- Modelling, analysis and optimal design of inductor coils, University of Kyoto, Department of Mathematics, Japan, October 21, 2004.

  • D. Hömberg, Widerstandsschweißen und Oberflächenhärtung von Stahl --- Modellierung, Analysis und optimale Steuerung, Colloquium of Sfb 393, Technische Universität Chemnitz, Institut für Mathematik, February 13, 2004.

  • O. Klein, Optimierung des Temperaturfeldes bei der Sublimationszüchtung von SiC Einkristallen, DGKK Arbeitskreis Angewandte Simulation in der Kristallzüchtung, February 5 - 6, 2004, Deutsche Gesellschaft für Kristallwachstum und Kristallzüchtung e.V., Volkach, February 5, 2004.

  • C. Meyer, O. Klein, P. Philip, A. Rösch, J. Sprekels, F. Tröltzsch, Optimal"-steuerung bei der Herstellung von SiC-Einkristallen, MathInside---Überall ist Mathematik, event of the DFG Research Center ``Mathematics for Key Technologies'' on the occasion of the Open Day of Urania, Berlin, September 13, 2003.

  • R. Henrion, W. Römisch, Hölder and Lipschitz stability of solution sets in programs with probabilistic constraints, 18th International Symposium on Mathematical Programming (ISMP 2003), August 18 - 22, 2003, Copenhagen, Denmark, August 18, 2003.

  • R. Henrion, Hölder and Lipschitz stability of solution sets in programs with probabilistic constraints, Charles University, Institute of Mathematics, Prague, Czech Republic, April 24, 2003.

  • D. Hömberg, Optimal design of inductor coils, 5th International Congress on Industrial and Applied Mathematics (ICIAM 2003), July 7 - 11, 2003, Sydney, Australia, July 10, 2003.

  • D. Hömberg, Surface hardening of steel --- Part I: Optimal design of inductor coils, 9th IEEE International Conference on Methods and Models in Automation and Robotics, August 25 - 28, 2003, Miedzyzdroje, Poland, August 26, 2003.

  External Preprints

  • P. Dvurechensky, A. Gasnikov, E. Gasnikova, S. Matsievsky, A. Rodomanov, I. Usik, Primal-dual method for searching equilibrium in hierarchical congestion population games, Preprint no. arXiv:1606.08988, Cornell University Library, arXiv.org, 2016.
    Abstract
    In this paper, we consider a large class of hierarchical congestion population games. One can show that the equilibrium in a game of such type can be described as a minimum point in a properly constructed multi-level convex optimization problem. We propose a fast primal-dual composite gradient method and apply it to the problem, which is dual to the problem describing the equilibrium in the considered class of games. We prove that this method allows to find an approximate solution of the initial problem without increasing the complexity.

  • R. Hildebrand, Spectrahedral cones generated by rank 1 matrices, Preprint no. arXiv:1409.4781, Cornell University Library, arXiv.org, 2014.

  • P.J.C. Dickinson, R. Hildebrand, Considering copositivity locally, Preprint no. 4315, Optimization Online, optimization-online.org, 2014.
    Abstract
    Let A be an element of the copositive cone COPn. A zero u of A is a nonnegative vector whose elements sum up to one and such that uTAu = 0. The support of u is the index set supp u  f1; : : : ; ng corresponding to the nonzero entries of u. A zero u of A is called minimal if there does not exist another zero v of A such that its support supp v is a strict subset of supp u. Our main result is a characterization of the cone of feasible directions at A, i.e., the convex cone KA of real symmetric nn matrices B such that there exists  > 0 satisfying A + B 2 COPn. This cone is described by a set of linear inequalities on the elements of B constructed from the set of zeros of A and their supports. This characterization furnishes descriptions of the minimal face of A in COPn, and of the minimal exposed face of A in COPn, by sets of linear equalities and inequalities constructed from the set of minimal zeros of A and their supports. In particular, we can check whether A lies on an extreme ray of COPn by examining the solution set of a system of linear equations. In addition, we deduce a simple necessary and sucient condition on the irreducibility of A with respect to a copositive matrix C. Here A is called irreducible with respect to C if for all  > 0 we have A ?? C 62 COPn.