René Henrion

On Convex Lower-Level Black-Box Constraints in Bilevel Optimization with an Application to Gas Market Models with Chance Constraints

  • Holger Heitsch
  • René Henrion
  • Thomas Kleinert
  • Martin Schmidt
    • Categories Applications - OR and Management Sciences, Cutting Plane Approaches, Stochastic Programming Tags , , , ,

    Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard to solve in theory and practice. In this paper, we add on the general difficulty of this class of problems by further incorporating convex black-box constraints in the lower level. For this … Read more

    Solving joint chance constrained problems using regularization and Benders’ decomposition

  • Lukáš Adam
  • Holger Heitsch
  • René Henrion
  • Martin Branda
    • Categories Stochastic Programming

    We consider stochastic programs with joint chance constraints with discrete random distribution. We reformulate the problem by adding auxiliary variables. Since the resulting problem has a non-regular feasible set, we regularize it by increasing the feasible set. We solve the regularized problem by iteratively solving a master problem while adding Benders’ cuts in a slave … Read more

    Optimal scenario generation and reduction in stochastic programming

  • René Henrion
  • Werner Romisch
    • Categories Semi-infinite Programming, Stochastic Programming Tags , , ,

    Scenarios are indispensable ingredients for the numerical solution of stochastic optimization problems. Earlier approaches for 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 on distances containing minimal information, i.e., on data appearing … Read more

    Joint dynamic probabilistic constraints with projected linear decision rules

  • Vincent Guigues
  • René Henrion
    • Categories Stochastic Programming

    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 … Read more

    Discrete Approximations of a Controlled Sweeping Process

  • Giovanni Colombo
  • René Henrion
  • Boris S. Mordukhovich
  • Nguyen Dinh Hoang
    • Categories Nonsmooth Optimization Tags , , , , ,

    The paper is devoted to the study of a new class of optimal control problems governed by the classical Moreau sweeping process with the new feature that the polyhedral moving set is not fixed while controlled by time-dependent functions. The dynamics of such problems is described by dissipative non-Lipschitzian differential inclusions with state constraints of … Read more

    About error bounds in metric spaces

  • Marian J. Fabian
  • René Henrion
  • Alexander Y. Kruger
  • Jiri V. Outrata
    • Categories Nonsmooth Optimization

    The paper presents a general primal space classification scheme of necessary and sufficient criteria for the error bound property incorporating the existing conditions. Several primal space derivative-like objects – slopes – are used to characterize the error bound property of extended-real-valued functions on metric sapces. CitationPublished in D. Klatte et al. (eds.), Operations Research Proceedings … Read more

    Some remarks on stability of generalized equations

  • René Henrion
  • Alexander Y. Kruger
  • Jiri V. Outrata
    • Categories Nonsmooth Optimization Tags , , ,

    The paper concerns the computation of the graphical derivative and the regular (Frechet) 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 C2 inequalities. Instead of the Linear Independence qualification condition, standardly used in this context, … Read more

    Error bounds: necessary and sufficient conditions

  • Marian J. Fabian
  • René Henrion
  • Alexander Y. Kruger
  • Jiri V. Outrata
    • Categories Nonsmooth Optimization

    The paper presents a general classiffication 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. CitationPublished in Set-Valued and Variational … Read more