Robust Optimization

Strictly and Γ-Robust Counterparts of Electricity Market Models: Perfect Competition and Nash-Cournot Equilibria

  • Anja Kramer
  • Vanessa Krebs
  • Martin Schmidt
    • Categories Finance and Economics, Game Theory, Robust Optimization Tags , , , ,

    This paper mainly studies two topics: linear complementarity problems for modeling electricity market equilibria and optimization under uncertainty. We consider both perfectly competitive and Nash–Cournot models of electricity markets and study their robustifications using strict robustness and the Γ-approach. For three out of the four combinations of economic competition and robustification, we derive algorithmically tractable … Read more

    Data-Driven Distributionally Robust Chance-Constrained Optimization with Wasserstein Metric

  • Ran Ji
  • Miguel A. Lejeune
    • Categories Robust Optimization, Second-Order Cone Programming, Stochastic Programming Tags , ,

    We study distributionally robust chance-constrained programming (DRCCP) optimization problems with data-driven Wasserstein ambiguity sets. The proposed algorithmic and reformulation framework applies to distributionally robust optimization problems subjected to individual as well as joint chance constraints, with random right-hand side and technology vector, and under two types of uncertainties, called uncertain probabilities and continuum of realizations. … Read more

    On the Optimality of Affine Policies for Budgeted Uncertainty Sets

  • Omar El Housni
  • Vineet Goyal
    • Categories Robust Optimization Tags , ,

    In this paper, we study the performance of affine policies for two-stage adjustable robust optimization problem with uncertain right hand side belonging to a budgeted uncertainty set. This is an important class of uncertainty sets widely used in practice where we can specify a budget on the adversarial deviations of the uncertain parameters from the … Read more

    Disjoint Bilinear Optimization: A Two-Stage Robust Optimization Perspective

  • Danique de Moor
  • Dick den Hertog
  • Ahmadreza Marandi
  • Lieven Vandenberghe
  • Jianzhe Zhen
    • Categories Robust Optimization Tags , , ,

    In this paper, we focus on a subclass of quadratic optimization problems, that is, disjoint bilinear optimization problems. We first show that disjoint bilinear optimization problems can be cast as two-stage robust linear optimization problems with fixed-recourse and right-hand-side uncertainty, which enables us to apply robust optimization techniques to solve the resulting problems. To this … Read more

    Tractable approximation of hard uncertain optimization problems

  • Aharon Ben-Tal
  • Frans J.C.T. de Ruiter
  • Dick den Hertog
  • Ernst Roos
  • Jianzhe Zhen
    • Categories Robust Optimization Tags , ,

    In many optimization problems uncertain parameters appear in a convex way, which is problematic as common techniques can only handle concave uncertainty. In this paper, we provide a systematic way to construct conservative approximations to such problems. Specifically, we reformulate the original problem as an adjustable robust optimization problem in which the nonlinearity of the … Read more

    Data-Driven Chance Constrained Programs over Wasserstein Balls

  • Zhi Chen
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Stochastic Programming Tags , ,

    We provide an exact deterministic reformulation for data-driven chance constrained programs over Wasserstein balls. For individual chance constraints as well as joint chance constraints with right-hand side uncertainty, our reformulation amounts to a mixed-integer conic program. In the special case of a Wasserstein ball with the $1$-norm or the $\infty$-norm, the cone is the nonnegative … Read more

    The Value of Randomized Solutions in Mixed-Integer Distributionally Robust Optimization Problems

  • Erick Delage
  • Ahmed Saif
    • Categories (Mixed) Integer Linear Programming, Robust Optimization Tags , ,

    Randomization refers to the process of taking decisions randomly according to the outcome of an independent randomization device such as a dice or a coin flip. The concept is unconventional, and somehow counterintuitive, in the domain of mathematical programming, where deterministic decisions are usually sought even when the problem parameters are uncertain. However, it has … Read more

    On Distributionally Robust Chance Constrained Programs with Wasserstein Distance

  • Weijun Xie
    • Categories Robust Optimization, Stochastic Programming

    This paper studies a distributionally robust chance constrained program (DRCCP) with Wasserstein ambiguity set, where the uncertain constraints should be satisfied with a probability at least a given threshold for all the probability distributions of the uncertain parameters within a chosen Wasserstein distance from an empirical distribution. In this work, we investigate equivalent reformulations and … Read more

    On the heavy-tail behavior of the distributionally robust newsvendor

  • Bikramjit Das
  • Karthik Natarajan
  • Anulekha Dhara
    • Categories Robust Optimization

    Since the seminal work of Scarf (1958) [A min-max solution of an inventory problem, Studies in the Mathematical Theory of Inventory and Production, pages 201-209] on the newsvendor problem with ambiguity in the demand distribution, there has been a growing interest in the study of the distributionally robust newsvendor problem. The optimal order quantity is … Read more

    Piecewise constant decision rules via branch-and-bound based scenario detection for integer adjustable robust optimization

  • Krzysztof Postek
  • Ward Romeijnders
    • Categories Integer Programming, Robust Optimization

    Multi-stage problems with uncertain parameters and integer decisions variables are among the most difficult applications of robust optimization (RO). The challenge in these problems is to find optimal here-and-now decisions, taking into account that the wait-and-see decisions have to adapt to the revealed values of the uncertain parameters. Postek and den Hertog (2016) and Bertsimas … Read more