Publications
Monographs

L. Ghezzi, D. Hömberg, Ch. Landry, eds., Math for the Digital Factory, 27 of Mathematics in Industry / The European Consortium for Mathematics in Industry, Springer International Publishing AG, Cham, 2017, x+348 pages, (Collection Published), DOI 10.1007/9783319639574 .

H. Heitsch, R. Henrion, H. Leövey, R. Mirkov, A. Möller, W. Römisch, I. WegnerSpecht, Chapter 13: Empirical Observations and Statistical Analysis of Gas Demand Data, in: Evaluating Gas Network Capacities, Th. Koch, B. Hiller, M.E. Pfetsch, L. Schewe, eds., MOSSIAM Series on Optimization, SIAM, Philadelphia, 2015, pp. 273290, (Chapter Published).

B. Hiller, Ch. Hayn, H. Heitsch, R. Henrion, H. Leövey, A. Möller, W. Römisch, Chapter 14: Methods for Verifying Booked Capacities, in: Evaluating Gas Network Capacities, Th. Koch, B. Hiller, M.E. Pfetsch, L. Schewe, eds., MOSSIAM Series on Optimization, SIAM, Philadelphia, 2015, pp. 291315, (Chapter 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).
Articles in Refereed Journals

M. Eigel, J. Neumann, R. Schneider, S. Wolf, Risk averse stochastic structural topology optimization, Computer Methods in Applied Mechanics and Engineering, 334 (2018), pp. 470482, DOI 10.1016/j.cma.2018.02.003 .
Abstract
A novel approach for riskaverse 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 highdimensional 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 riskaware measure, the Conditional Value at Risk (CVaR) is used in the cost functional during the minimization procedure. Since the treatment of such highdimensional 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. 
A. Gasnikov, P. Dvurechensky, M. Zhukovskii, S. Kim, S. Plaunov, D. Smirnov, F. Noskov, About the power law of the PageRank vector distribution. Part 2. BackleyOsthus model, power law verification for this model and setup of real search engines, Numerical Analysis and Applications, 11 (2018), pp. 1632, DOI 10.1134/S1995423918010032 .

P. Dvurechensky, A. Gasnikov, A. Lagunovskaya, Parallel algorithms and probability of large deviation for stochastic convex optimization problems, Numerical Analysis and Applications, 11 (2018), pp. 3337, DOI 10.1134/S1995423918010044 .

T. González Grandón, H. Heitsch, R. Henrion, A joint model of probabilistic/robust constraints for gas transport management in stationary networks, Computational Management Science, 14 (2017), pp. 443460, DOI 10.1007/s1028701702847 .
Abstract
We present a novel mathematical algorithm to assist gas network operators in managing uncertainty, while increasing reliability of transmission and supply. As a result, we solve an optimization problem with a joint probabilistic constraint over an infinite system of random inequalities. Such models arise in the presence of uncertain parameters having partially stochastic and partially nonstochastic character. The application that drives this new approach is a stationary network with uncertain demand (which are stochastic due to the possibility of fitting statistical distributions based on historical measurements) and with uncertain roughness coefficients in the pipes (which are uncertain but nonstochastic due to a lack of attainable measurements). We study the sensitivity of local uncertainties in the roughness coefficients and their impact on a highly reliable network operation. In particular, we are going to answer the question, what is the maximum uncertainty that is allowed (shaping a 'maximal' uncertainty set) around nominal roughness coefficients, such that random demands in a stationary gas network can be satisfied at given high probability level for no matter which realization of true roughness coefficients within the uncertainty set. One ends up with a constraint, which is probabilistic with respect to the load of gas and robust with respect to the roughness coefficients. We demonstrate how such constraints can be dealt with in the framework of the socalled sphericradial decomposition of multivariate Gaussian distributions. The numerical solution of a corresponding optimization problem is illustrated. The results might assist the network operator with the implementation of costintensive roughness measurements. 
A.L. Diniz, R. Henrion, On probabilistic constraints with multivariate truncated Gaussian and lognormal distributions, Energy Systems, 8 (2017), pp. 149167, DOI 10.1007/s1266701501806 .

A. Gasnikov, E. Gasnikova, P. Dvurechensky, A. Mohammed, E. Chernousova, About the power law of the PageRank vector component distribution. Part 1. Numerical methods for finding the PageRank vector (Original Russian text published in Sib. Zh. Vychisl. Mat., 20 (2017), pp. 359378), Numerical Analysis and Applications, 10 (2017), pp. 299312.

V. Guigues, R. Henrion, Joint dynamic probabilistic constraints with projected linear decision rules, Optimization Methods & Software, 32 (2017), pp. 10061032.
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 waitandsee 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. 6387, DOI 10.1137/16M1061308 .
Abstract
We consider probability functions of parameterdependent 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. 
H. Heitsch, H. Leövey, W. Römisch, Are quasiMonte Carlo algorithms efficient for twostage stochastic programs?, Computational Optimization and Applications. An International Journal, 65 (2016), pp. 567603.
Abstract
QuasiMonte Carlo algorithms are studied for designing discrete approximations of twostage linear stochastic programs with random righthand side and continuous probability distribution. The latter should allow for a transformation to a distribution with independent marginals. The twostage integrands are piecewise linear, but neither smooth nor lie in the function spaces considered for QMC error analysis. We show that under some weak geometric condition on the twostage model all terms of their ANOVA decomposition, except the one of highest order, are continuously differentiable and that first and second order ANOVA terms have mixed first order partial derivatives. Hence, randomly shifted lattice rules (SLR) may achieve the optimal rate of convergence not depending on the dimension if the effective superposition dimension is at most two. We discuss effective dimensions and dimension reduction for twostage integrands. The geometric condition is shown to be satisfied almost everywhere if the underlying probability distribution is normal and principal component analysis (PCA) is used for transforming the covariance matrix. Numerical experiments for a large scale twostage stochastic production planning model with normal demand show that indeed convergence rates close to the optimal are achieved when using SLR and randomly scrambled Sobol' point sets accompanied with PCA for dimension reduction. 
R. Hildebrand, Spectrahedral cones generated by rank 1 matrices, Journal of Global Optimization. An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering, 64 (2016), pp. 349397.

C. Gotzes, H. Heitsch, R. Henrion, R. Schultz, On the quantification of nomination feasibility in stationary gas networks with random load, Mathematical Methods of Operations Research, 84 (2016), pp. 427457.
Abstract
The paper considers the computation of the probability of feasible load constellations in a stationary gas network with uncertain demand. More precisely, a network with a single entry and several exits with uncertain loads is studied. Feasibility of a load constellation is understood in the sense of an existing flow meeting these loads along with given pressure bounds in the pipes. In a first step, feasibility of deterministic exit loads is characterized algebraically and these general conditions are specified to networks involving at most one cycle. This prerequisite is essential for determining probabilities in a stochastic setting when exit loads are assumed to follow some (joint) Gaussian distribution when modeling uncertain customer demand. The key of our approach is the application of the sphericradial decomposition of Gaussian random vectors coupled with Quasi MonteCarlo sampling. This approach requires an efficient algorithmic treatment of the mentioned algebraic relations moreover depending on a scalar parameter. Numerical results are illustrated for different network examples and demonstrate a clear superiority in terms of precision over simple generic MonteCarlo sampling. They lead to fairly accurate probability values even for moderate sample size. 
A.V. Gasnikov, P. Dvurechensky, Y.E. Nesterov, Stochastic gradient methods with inexact oracle, Proceedings of Moscow Institute of Physics and Technology, 8:1 (2016), pp. 4191.

A. Gasnikov, P. Dvurechensky, I. Usmanova, On accelerated randomized methods, Proceedings of Moscow Institute of Physics and Technology, 8:2 (2016), pp. 67100.

A. Gasnikov, P. Dvurechensky, Stochastic intermediate gradient method for convex optimization problems, Doklady Mathematics. Maik Nauka/Interperiodica Publishing, Moscow. English. Translation of the Mathematics Section of: Doklady Akademii Nauk. (Formerly: Russian Academy of Sciences. Doklady. Mathematics)., 93 (2016), pp. 148151.

P. Dvurechensky, A. Gasnikov, Stochastic intermediate gradient method for convex problems with inexact stochastic oracle, Journal of Optimization Theory and Applications, 171 (2016), pp. 121145.

A. Gasnikov, E. Gasnikova, P. Dvurechensky, E. Ershov, A. Lagunovskaia, Searching for the stochastic equilibria in the transport models of equilibrium flow distribution (in Russian), Proceedings of Moscow Institute of Physics and Technology, 7 (2015), pp. 114128.

A. Gasnikov, P. Dvurechensky, D. Kamzolov, Y. Nesterov, V. Spokoiny, P. Stetsyuk, A. Suvorikova, A. Chernov, Searching for equilibriums in multistage transport models (in Russian), Proceedings of Moscow Institute of Physics and Technology, 7 (2015), pp. 143155.

I. Bremer, R. Henrion, A. Möller, Probabilistic constraints via SQP solver: Application to a renewable energy management problem, Computational Management Science, 12 (2015), pp. 435459.
Abstract
The aim of this paper is to illustrate the efficient solution of nonlinear optimization problems with joint probabilistic constraints by means of an SQP method. Here, the random vector is assumed to obey some multivariate Gaussian distribution. The numerical solution approach is applied to a renewable energy management problem. We consider a coupled system of hydro and wind power production used in order to satisfy some local demand of energy and to sell/buy excessive or missing energy on a dayahead and intraday market, respectively. A short term planning horizon of 2 days is considered and only wind power is assumed to be random. In the first part of the paper, we develop an appropriate optimization problem involving a probabilistic constraint reflecting demand satisfaction. Major attention will be payed to formulate this probabilistic constraint not directly in terms of random wind energy produced but rather in terms of random wind speed, in order to benefit from a large data base for identifying an appropriate distribution of the random parameter. The second part presents some details on integrating Genz' code for Gaussian probabilities of rectangles into the environment of the SQP solver SNOPT. The procedure is validated by means of a simplified optimization problem which by its convex structure allows to estimate the gap between the numerical and theoretical optimal values, respectively. In the last part, numerical results are presented and discussed for the original (nonconvex) optimization problem. 
TH. Arnold, R. Henrion, A. Möller, S. Vigerske, A mixedinteger stochastic nonlinear optimization problem with joint probabilistic constraints, Pacific Journal of Optimization. An International Journal, 10 (2014), pp. 520.
Abstract
We illustrate the solution of a mixedinteger 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. 
K. Emich, R. Henrion, W. Römisch, Conditioning of linearquadratic twostage stochastic optimization problems, Mathematical Programming. A Publication of the Mathematical Programming Society, 148 (2014), pp. 201221.
Abstract
In this paper a condition number for linearquadratic twostage 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 secondorder subdifferential recently proved by Mordukhovich and Rockafellar plays a crucial role. The obtained results are illustrated for the example of twostage stochastic optimization problems with simple recourse. 
W. VAN Ackooij, R. Zorgati, R. Henrion, A. Möller, Joint chance constrained programming for hydro reservoir management, Optimization and Engineering. International Multidisciplinary Journal to Promote Optimization Theory & Applications in Engineering Sciences, 15 (2014), pp. 509531.

W. VAN Ackooij, R. Henrion, Gradient formulae for nonlinear probabilistic constraints with Gaussian and Gaussianlike distributions, SIAM Journal on Optimization, 24 (2014), pp. 18641889.
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 sphericalradial 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.
Contributions to Collected Editions

TH. Arnold, R. Henrion, M. Grötschel, W. Römisch ET AL., B4  A Jack of all trades? Solving stochastic mixedinteger nonlinear constraint programs, 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. 135146.
Preprints, Reports, Technical Reports

R. Henrion, W. Römisch, Problembased optimal scenario generation and reduction in stochastic programming, Preprint no. 2485, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2485 .
Abstract, PDF (259 kByte)
Scenarios are indispensable ingredients for the numerical solution of stochastic programs. Earlier approaches to optimal scenario generation and reduction are based on stability arguments involving distances of probability measures. In this paper we review those ideas and suggest to make use of stability estimates based only on problem specific data. For linear twostage stochastic programs we show that the problembased approach to optimal scenario generation can be reformulated as best approximation problem for the expected recourse function which in turn can be rewritten as a generalized semiinfinite program. We show that the latter is convex if either righthand sides or costs are random and can be transformed into a semiinfinite program in a number of cases. We also consider problembased optimal scenario reduction for twostage models and optimal scenario generation for chance constrained programs. Finally, we discuss problembased scenario generation for the classical newsvendor problem. 
A. Hantoute, R. Henrion, P. PérezAros, Subdifferential characterization of probability functions under Gaussian distribution, Preprint no. 2478, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2478 .
Abstract, PDF (282 kByte)
Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth. This fact motivates the consideration of subdifferentials for such typically just continuous functions. The aim of this paper is to provide subdifferential formulae of such functions in the case of Gaussian distributions for possibly infinitedimensional decision variables and nonsmooth (locally Lipschitzian) input data. These formulae are based on the sphericradial decomposition of Gaussian random vectors on the one hand and on a cone of directions of moderate growth on the other. By successively adding additional hypotheses, conditions are satisfied under which the probability function is locally Lipschitzian or even differentiable. 
L. Adam, M. Branda, H. Heitsch, R. Henrion, Solving joint chance constrained problems using regularization and Benders' decomposition, Preprint no. 2471, WIAS, Berlin, 2018, DOI 10.20347/WIAS.PREPRINT.2471 .
Abstract, PDF (236 kByte)
In this paper we investigate stochastic programms with joint chance constraints. We consider discrete scenario set and reformulate the problem by adding auxiliary variables. Since the resulting problem has a difficult feasible set, we regularize it. To decrease the dependence on the scenario number, we propose a numerical method by iteratively solving a master problem while adding Benders cuts. We find the solution of the slave problem (generating the Benders cuts) in a closed form and propose a heuristic method to decrease the number of cuts. We perform a numerical study by increasing the number of scenarios and compare our solution with a solution obtained by solving the same problem with continuous distribution. 
P. Dupuis, V. Laschos, K. Ramanan, Exit time risksensitive stochastic control problems related to systems of cooperative agents, Preprint no. 2407, WIAS, Berlin, 2017, DOI 10.20347/WIAS.PREPRINT.2407 .
Abstract, PDF (447 kByte)
We study sequences, parametrized by the number of agents, of exit time stochastic control problems with risksensitive costs structures generate by unbounded costs. We identify a fully characterizing assumption, under which, each of them corresponds to a riskneutral stochastic control problem with additive cost, and also to a riskneutral stochastic control problem on the simplex, where the specific information about the state of each agent can be discarded. We finally prove that, under some additional assumptions, the sequence of value functions converges to the value function of a deterministic control problem. 
R. Hildebrand, J.G.M. Schoenmakers, J. Zhang, F. Dickmann, Regression based duality approach to optimal control with application to hydro electricity storage, Preprint no. 2330, WIAS, Berlin, 2016, DOI 10.5072/WIAS.PREPRINT.2330 .
Abstract, PDF (341 kByte)
In this paper we consider the problem of optimal control of stochastic processes. We employ the dual martingale method brought forward in [Brown, Smith, and Sun, 2010]. The martingale constituting the solution of the dual problem is determined by linear regression within a MonteCarlo approach. We apply the solution algorithm to a model of a hydro electricity storage and production system coupled with a model of the electricity wholesale market. 
R. Hildebrand, Copositive matrices with circulant zero pattern, Preprint no. 2241, WIAS, Berlin, 2016.
Abstract, PDF (335 kByte)
Let n be an integer not smaller than 5 and let u1,...,un be nonnegative real nvectors such that the indices of their positive elements form the sets 1,2,...,n2,2,3,...,n1,...,n,1,...,n3, respectively. Here each index set is obtained from the previous one by a circular shift. The set of copositive forms which vanish on the vectors u1,...,un is a face of the copositive cone. We give an explicit semidefinite description of this face and of its subface consisting of positive semidefinite matrices, and study their properties. If the vectors u1,...,un and their positive multiples exhaust the zero set of an exceptional copositive form belonging to this face, then we call this form regular, otherwise degenerate. We show that degenerate forms are always extremal, and regular forms can be extremal only if n is odd. We construct explicit examples of extremal degenerate forms for any order n, and examples of extremal regular forms for any odd order n. The set of all degenerate forms, i.e., defined by different collections u1,...,un of zeros, is a submanifold of codimension 2n, the set of all regular forms a submanifold of codimension n.
Talks, Poster

H. Heitsch, A probabilistic approach to optimization problems in gas transport networks, SESO 2017 International Thematic Week ``Smart Energy and Stochastic Optimization'', May 30  June 1, 2017, ENSTA ParisTech and École des Ponts ParisTech, Paris, France, June 1, 2017.

H. Heitsch, A probabilistic approach to optimization problems in gas transport networks, CIMWIAS Workshop ``Topics in Applied Analysis and Optimisation'', December 6  8, 2017, International Center for Mathematics, University of Lisbon, Portugal, December 6, 2017.

H. Heitsch, On probabilistic capacity maximization in stationary gas networks, 21st Conference of the International Federation of Operational Research Societies (IFORS 2017), Invited Session TB20 ``Optimization of Gas Networks 2'', July 17  21, 2017, Quebec, Canada, July 18, 2017.

P. Dvurechensky, A unified view on accelerated randomized optimization methods: Coordinate descent, directional search, derivativefree method, Foundations of Computational Mathematics (FoCM 2017), Barcelona, Spain, July 17  19, 2017.

R. Henrion, Contraintes en probabilité: Formules du gradient et applications, Workshop ``MASMODE 2017'', Institut Henri Poincaré, Paris, France, January 9, 2017.

R. Henrion, On Mstationary 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, On a joint model for probabilistic/robust constraints with an application to gas networks under uncertainties, Workshop ``Models and Methods of Robust Optimization'', March 9  10, 2017, FraunhoferInstitut für Techno und Wirtschaftsmathematik ITWM, Kaiserslautern, March 10, 2017.

R. Henrion, Optimization problems under robust constraints with applications to gas networks under uncertainty, The Eighth AustraliaChina Workshop on Optimization (ACWO 2017), December 4, 2017, Curtin University, Perth, Australia, December 4, 2017.

R. Henrion, Probabilistic constraints in infinite dimensions, Universität Wien, Institut für Statistik und Operations Research, Austria, November 6, 2017.

R. Henrion, Probabilistic constraints: Convexity issues and beyond, XII International Symposium on Generalized Convexity and Monotonicity, August 27  September 2, 2017, Hajdúszoboszló, Hungary, August 29, 2017.

R. Henrion, Probabilistic programming in infinite dimensions, The South Pacific Optimization Meeting in Western Australia 2017 (SPOM in WA 2017), December 8  10, 2017, Curtin University, Perth, Australia, December 9, 2017.

R. Henrion, Probabilistic programming: Structural properties and applications, Control and Optimization Conference on the occasion of Frédéric Bonnans 60th birthday, November 15  17, 2017, Electricité de France, Palaiseau, France, November 17, 2017.

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

R. Henrion, Subdifferential characterization of Gaussian probability functions, SESO 2017 International Thematic Week ``Smart Energy and Stochastic Optimization'', May 30  June 1, 2017, ENSTA ParisTech and École des Ponts ParisTech, Paris, France, June 1, 2017.

R. Henrion, Subdifferential estimates for Gaussian probability functions, HCM Workshop: Nonsmooth Optimization and its Applications, May 15  19, 2017, Hausdorff Center for Mathematics, Bonn, May 17, 2017.

R. Henrion, Subdifferential of probability functions under Gaussian distribution, The Second Pacific Optimization Conference (POC2017), December 4  7, 2017, Curtin University, Perth, Australia, December 6, 2017.

H. Heitsch, Nonlinear probabilistic constraints in gas transportation problems, WIASPGMO Workshop on Nonsmooth and Stochastic Optimization with Applications to Energy Management, May 10  12, 2016, WIAS Berlin, Australia, May 11, 2016.

H. Heitsch, Optimization in gas transport networks using nonlinear probabilistic constraints, XIV International Conference on Stochastic Programming (ICSP 2016), Thematic Session: Probabilistic Constraints: Applications and Theory, June 25  July 1, 2016, Búzios, Brazil, June 28, 2016.

R. Hildebrand, Canonical barriers on convex cones, Oberseminar Geometrische Analysis, Johann Wolfgang GoetheUniversität Frankfurt am Main, Fachbereich Mathematik, April 26, 2016.

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

I. Bremer, Dealing with probabilistic constraints under multivariate normal distribution in a standard SQP solver by using Genz' method, WIASPGMO Workshop on Nonsmooth and Stochastic Optimization with Applications to Energy Management, May 10  12, 2016, WIAS Berlin, May 11, 2016.

R. Henrion, (Sub)Gradient formulae for Gaussian probability functions, XIV International Conference on Stochastic Programming (ICSP 2016), Thematic Session: Probabilistic Constraints: Applications and Theory, June 25  July 1, 2016, Búzios, Brazil, June 28, 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, Formules du gradient pour des fonctions probabilistes Gaussiennes, Workshop on Offshore Wind Generation, September 9, 2016, Electricité de France R&D, Paris, France, September 9, 2016.

R. Henrion, Initiation aux problèmes d'optimisation sous contraintes en probabilité, Workshop ``Optimisation en Milieu Aléatoire'', November 8, 2016, Institut des Sciences Informatiques et de leurs Interactions, GdR 720 ISIS (Information, Signal, Image et ViSion), Paristech Télécom, Paris, France, November 8, 2016.

R. Henrion, Optimisation sous contraintes en probabilité, Séminaire du Groupe de Travail ``Modèles Stochastiques en Finance'', Ecole Nationale Supérieure des Techniques Avancées (ENSTA) ParisTech, Palaiseau, France, November 28, 2016.

R. Henrion, Robuststochastic optimization problems in stationary gas networks, Conference ``Mathematics of Gas Transport'', October 6  7, 2016, Zuse Institut Berlin, October 6, 2016.

H. Heitsch, Optimization of booked capacity in gas transport networks using nonlinear probabilistic constraints, 2nd International Symposium on Mathematical Programming (ISMP 2015), Cluster ``Optimization in Energy Systems'', July 13  17, 2015, Pittsburgh, USA, July 17, 2015.

R. Hildebrand, Geometry of barriers for 3dimensional cones, Optimization and Applications in Control and Data Science, May 13  15, 2015, Moscow Institute of Physics and Technology, PreMoLab, Moscow, Russian Federation, May 15, 2015.

R. Hildebrand, Rank 1 generated spectrahedral cones, Frontiers of High Dimensional Statistics, Optimization, and Econometrics, February 26  27, 2015, Higher School of Economics, Moscow, Russian Federation, February 26, 2015.

R. Hildebrand , Optimizing strategies in energy and storage markets, Matheon Center Days, Technische Universität Berlin, April 16, 2015.

P. Dvurechensky, Semisupervised pagerank model learning with gradientfree optimization methods, Traditional Youth School ``Control, Information and Optimization'', June 14  20, 2015, Moscow, Russian Federation, June 17, 2015.

P. Dvurechensky, Stochastic intermediate gradient method: Convex and strongly convex cases, Information Technologies and Systems 2015, September 6  11, 2015, Russian Academy of Sciences, Institute for Information Transmission Problems, Sochi, Russian Federation, September 9, 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, Conditioning of linearquadratic twostage 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.

R. Henrion, Application of chance constraints in a coupled model of hydrowind energy production, Charles University in Prague, Faculty of Mathematics and Physics, Czech Republic, March 6, 2014.

R. Henrion, Application of probabilistic constraints to problems of energy management under uncertainty, Eidgenössische Technische Hochschule Zürich, Power Systems Laboratory, Switzerland, September 30, 2014.

R. Henrion, Conditioning of linearquadratic twostage 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, Gradient formulae in probabilistic programming, Conference on Optimization & Practices in Industry (PGMOCOPI'14), October 28  31, 2014, Ecole Polytechnique, Paris, France, October 29, 2014.

R. Henrion, Gradient formulae in probabilistic programming, Université Paul Sabatier, Laboratoire d'analyse et d'architecture des systèmes, Toulouse, France, December 8, 2014.

R. Henrion, Nonlinear programming for solving chance constrained optimization problems: Application to renewable energies, Winter School on Stochastic Programming with Applications in Energy, Finance and Insurance, March 23  28, 2014, Bad Hofgastein, Austria, March 25, 2014.

R. Henrion, Probabilistic constraints in hydro reservoir management, XIII Symposium of Specialists in Electric Operational and Expansion Planning (SEPOPE), May 18  21, 2014, Foz do Iguassu, Brazil, May 19, 2014.

R. Henrion, Probabilistic constraints via nonlinear programming: Application to energy management problems, Euro Mini Conference on Stochastic Programming and Energy Applications (EuroCSP2014), September 24  26, 2014, Institut Henri Poincaré, Paris, France, September 25, 2014.

R. Henrion, Probabilistic constraints: A structureoriented introduction, Optimization and Applications Seminar, Eidgenössische Technische Hochschule Zürich, Switzerland, September 29, 2014.

R. Henrion, Problèmes d'optimisation sous contraintes en probabilité: une initiation, December 9  10, 2014, Université Paul Sabatier, Institut de Mathématiques de Toulouse, France.
External Preprints

P. Dvurechensky, A. Gasnikov, E. Gorbunov, An accelerated directional derivative method for smooth stochastic convex optimization, Preprint no. arXiv:1804.02394, Cornell University Library, arXiv.org, 2018.

P. Dvurechensky, A. Gasnikov, E. Gorbunov, An accelerated method for derivativefree smooth stochastic convex optimization, Preprint no. arXiv: 1802.09022, Cornell University Library, arXiv.org, 2018.
Abstract
We consider an unconstrained problem of minimization of a smooth convex function which is only available through noisy observations of its values, the noise consisting of two parts. Similar to stochastic optimization problems, the first part is of a stochastic nature. On the opposite, the second part is an additive noise of an unknown nature, but bounded in the absolute value. In the twopoint feedback setting, i.e. when pairs of function values are available, we propose an accelerated derivativefree algorithm together with its complexity analysis. The complexity bound of our derivativefree algorithm is only by a factor of n??? larger than the bound for accelerated gradientbased algorithms, where n is the dimension of the decision variable. We also propose a nonaccelerated derivativefree algorithm with a complexity bound similar to the stochasticgradientbased algorithm, that is, our bound does not have any dimensiondependent factor. Interestingly, if the solution of the problem is sparse, for both our algorithms, we obtain better complexity bound if the algorithm uses a 1norm proximal setup, rather than the Euclidean proximal setup, which is a standard choice for unconstrained problems.