WIAS–PGMO Workshop on Nonsmooth and Stochastic Optimization

Humboldt-Universität zu Berlin

Johann von Neumann-Haus
Rudower Chaussee 25
Humboldt-Kabinett

Tuesday, June 26, 2018

9:30 am — 6:00 pm


Rudow

Organizers


Schedule

Time Tuesday, June 26th 2018
09:30 - 10:00 Coffee
Humboldt-Kabinett
10:00 - 10:30 Welcome
René Henrion
10:30 - 11:00 Talk 1
N.N.
11:00 - 11:30 Talk 2
N.N.
11:30 - 12:00 Coffee break
Humboldt-Kabinett
12:00 - 12:30 Talk 3
N.N.
12:30 - 13:00 Talk 4
N.N.
13:00 - 14:30 Lunch break
Caffè & Ess Bar Kamee
14:30 - 15:00 Talk 5
N.N.
15:00 - 15:30 Talk 6
N.N.
15:30 - 16:00 Talk 7
N.N.
16:00 - 16:30 Coffee break
Humboldt-Kabinett
16:30 - 17:00 Talk 8
N.N.
17:00 - 17:30 Talk 9
N.N.
17:30 - 18:00 Talk 10
N.N.
18:00 - 21:00 Get-together
Humboldt-Kabinett

Talks

  • Christian Grossmann, Technische Universität Dresden:


  • Michael Hintermüller, Weierstrass Institute Berlin:


  • Abderrahim Jourani, University of Bourgoge Dijon:


  • Diethard Klatte, University of Zurich: Isolated calmness of Hölder and Lipschitz type in nonlinear optimization
    In this talk, conditions for isolated calmness and isolated Hölder calmness of stationary solutions and local minimizers will be discussed. In the 1980ies and 1990ies, stability of this type was studied in many publications, but focussed on local minimizers for smooth and nonsmooth nonlinear programs under perturbations. Some linear or quadratic growth condition for the objective function and suitable constraints qualifications were usually the basic assumptions; applications and extensions to stability analysis of stochastic programs were given at that time by W. Römisch, R. Schultz and other authors. For the "classical" theory which studies also stationary solutions and more general classes of variational problems, we refer, e.g., to the monographs by F. Bonnans, A. Shapiro (2000) and D. Klatte, B. Kummer (2002). Recently, Helmut Gfrerer and the author came back to the classical approach, see, e.g., our common paper in Mathematical Programming 158 (2016). The purpose of this talk is to present and discuss refinements of well-known results and extensions to mathematical programs with equilibrium constraints (MPECs) by using a new type of constraint qualifications.

  • Boris Mordukhovich, Wayne State University Detroit: Extended Euler-Lagrange and Hamiltonian Conditions in Optimal Control of Sweeping Processes with Controlled Moving Sets
    This talk concerns optimal control problems for a class of sweeping processes governed by discontinuous unbounded differential inclusions that are described via normal cone mappings to controlled moving sets. Largely motivated by applications to hysteresis, we consider a general setting where moving sets are given as inverse images of closed subsets of finite-dimensional spaces under nonlinear differentiable mappings dependent on both state and control variables. Developing the method of discrete approximations and employing generalized differential tools of first-order and second-order variational analysis allow us to derive nondegenerate necessary optimality conditions for such problems in extended Euler-Lagrange and Hamiltonian forms involving the Hamiltonian maximization. The latter conditions of the Pontryagin Maximum Principle type are the first in the literature for optimal control of sweeping processes with control-dependent moving sets. Based on the joint work with Nguyen Hoang (University of Concepción, Chile).

  • Jiří Outrata, Czech Academy of Sciences Prag: On Cournot-Nash-Walras equilibria and their computation
    In this talk we consider a model of Cournot-Nash-Walras (CNW)equilibrium, where the Cournot-Nash concept is used to capture equilibrium of an oligopolistic market with non-cooperative players/firms. They share a certain amount of a so-called rare resource needed for their production, and the Walras equilibrium determines the price of that rare resource. We prove the existence of CNW equilibria under reasonable conditions and examine various numerical approaches for their computation. Finally, we demonstrate remarkably stable behavior of CNW equilibria with respect to small perturbations of problem data.

  • Alois Pichler, Technische Universität Chemnitz:


  • Rüdiger Schultz, University of Duisburg-Essen:


  • Caren Tischendorf, Humboldt-Universität zu Berlin:


  • Fredi Tröltzsch, Technische Universität Berlin: Optimal time delays in a class of reaction-diffusion equations
    A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best approximation of a desired state function. The differentiability of the mapping is proved that associates the solution of the delay equationto the vector of weights and delays. Based on an adjoint calculus, first-order necessary optimality conditions are derived. Numerical test examples show the applicability of the concept of optimizing time delays. This is joint work with Eduardo Casas and Mariano Mateos.

Participants


  • Tatiana González Grandón
  • Christian Grossmann
  • Nicole Gröwe-Kuska
  • Holger Heitsch
  • René Henrion
  • Michael Hintermüller
  • Abderrahim Jourani
  • Jutta Kerger
  • Diethard Klatte
  • Chistian Küchler
  • René Lamour
  • Hernan Leovey
  • Roswitha März
  • Andris Möller
  • Boris Mordukhovich
  • Ivo Nowak
  • Jiří Outrata
  • Alois Pichler
  • Ute Römisch
  • Werner Römisch
  • Rüdiger Schultz
  • Caren Tischendorf
  • Fredi Tröltzsch
  • Isabel Wegner-Specht
  • Sponsors

    This workshop benefits from the support of the FMJH Program Gaspard Monge in optimization and operation research (PGMO), from the support to this program from EDF, and, by the support of the Weierstrass Institute Berlin.

    WIAS-logo
    Weierstrass Institute Berlin
      Fondation Mathématique Jacques Hadamard