Stochastic Programming

Two-stage Stochastic Programming under Multivariate Risk Constraints with an Application to Humanitarian Relief Network Design

  • Simge Küçükyavuz
  • Merve Merakli
  • Nilay Noyan
    • Categories Stochastic Programming

    In this study, we consider two classes of multicriteria two-stage stochastic programs in finite probability spaces with multivariate risk constraints. The first-stage problem features a multivariate stochastic benchmarking constraint based on a vector-valued random variable representing multiple and possibly conflicting stochastic performance measures associated with the second-stage decisions. In particular, the aim is to ensure … Read more

    Distributionally Robust Reward-risk Ratio Programming with Wasserstein Metric

  • Yongchao Liu
  • Xinmin Yang
  • Jin Zhang
  • Yong Zhao
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    Reward-risk ratio (RR) is a very important stock market definition. In recent years, people extend RR model as distributionally robust reward-risk ratio (DRR) to capture the situation that the investor does not have complete information on the distribution of the underlying uncertainty. In this paper, we study the DRR model where the ambiguity on the … Read more

    Second-order cone programming formulation for two player zero-sum game with chance constraints

  • Abdel Lisser
  • Vikas Vikram Singh
    • Categories Game Theory, Stochastic Programming Tags , , , ,

    We consider a two player finite strategic zero-sum game where each player has stochastic linear constraints. We formulate the stochastic constraints of each player as chance constraints. We show the existence of a saddle point equilibrium if the row vectors of the random matrices, defining the stochastic constraints of each player, are elliptically symmetric distributed … Read more

    Distributionally robust chance constrained optimal power flow with renewables: A conic reformulation

  • Shabbir Ahmed
  • Weijun Xie
    • Categories Applications - Science and Engineering, Robust Optimization, Stochastic Programming

    The uncertainty associated with renewable energy sources introduces significant challenges in optimal power flow (OPF) analysis. A variety of new approaches have been proposed that use chance constraints to limit line or bus overload risk in OPF models. Most existing formulations assume that the probability distributions associated with the uncertainty are known a priori or … Read more

    Statistical inference and hypotheses testing of risk averse stochastic programs

  • Vincent Guigues
  • Alexander Shapiro
  • Volker Krätschmer
    • Categories Stochastic Programming Tags , , , , ,

    We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value when the stochastic program is expressed in terms of a law invariant coherent risk measure having a discrete Kusuoka representation. The obtained results … Read more

    Joint rectangular geometric chance constrained programs

  • Zhiping Chen
  • Abdel Lisser
  • Jia Liu
  • Chuan Xu
    • Categories Stochastic Programming Tags , , ,

    This paper discusses joint rectangular geometric chance constrained programs. When the stochastic parameters are elliptically distributed and pairwise independent, we present a reformulation of the joint rectangular geometric chance constrained programs. As the reformulation is not convex, we propose new convex approximations based on variable transformation together with piecewise linear approximation method. Our results show … Read more

    Combining Penalty-based and Gauss-Seidel Methods for solving Stochastic Mixed-Integer Problems

  • Eberhard Andrew
  • Brian Dandurand
  • Fabricio Oliveira
  • Jeffrey Christiansen
    • Categories Stochastic Programming Tags , , , ,

    In this paper, we propose a novel decomposition approach for mixed-integer stochastic programming (SMIP) problems that is inspired by the combination of penalty-based Lagrangian and block Gauss-Seidel methods (PBGS). In this sense, PBGS is developed such that the inherent decomposable structure that SMIPs present can be exploited in a computationally efficient manner. The performance of … Read more

    Decision Rule Bounds for Two-Stage Stochastic Bilevel Programs

  • Daniel Kuhn
  • Ihsan Yanıkoğlu
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    We study stochastic bilevel programs where the leader chooses a binary here-and-now decision and the follower responds with a continuous wait-and-see-decision. Using modern decision rule approximations, we construct lower bounds on an optimistic version and upper bounds on a pessimistic version of the leader’s problem. Both bounding problems are equivalent to explicit mixed-integer linear programs … Read more

    Ambiguous Chance-Constrained Binary Programs under Mean-Covariance Information

  • Ruiwei Jiang
  • Siqian Shen
  • Yiling Zhang
    • Categories 0-1 Programming, Second-Order Cone Programming, Stochastic Programming

    We consider chance-constrained binary programs, where each row of the inequalities that involve uncertainty needs to be satis ed probabilistically. Only the information of the mean and covariance matrix is available, and we solve distributionally robust chance-constrained binary programs (DCBP). Using two different ambiguity sets, we equivalently reformulate the DCBPs as 0-1 second-order cone (SOC) programs. … Read more

    Efficient methods for several classes of ambiguous stochastic programming problems under mean-MAD information

  • Dick den Hertog
  • Krzysztof Postek
  • Ward Romeijnders
  • Maarten H. van der Vlerk
    • Categories Robust Optimization, Stochastic Programming

    We consider decision making problems under uncertainty, assuming that only partial distributional information is available – as is often the case in practice. In such problems, the goal is to determine here-and-now decisions, which optimally balance deterministic immediate costs and worst-case expected future costs. These problems are challenging, since the worst-case distribution needs to be … Read more