Robust Optimization

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

    Maximizing a class of utility functions over the vertices of a polytope

  • Alper Atamturk
  • Andrés Gómez
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Stochastic Programming Tags , , , , , , , ,

    Given a polytope X, a monotone concave univariate function g, and two vectors c and d, we study the discrete optimization problem of finding a vertex of X that maximizes the utility function c’x + g(d’x). This problem has numerous applications in combinatorial optimization with a probabilistic objective, including estimation of project duration with stochastic … Read more

    A Copositive Approach for Two-Stage Adjustable Robust Optimization with Uncertain Right-Hand Sides

  • Samuel Burer
  • Guanglin Xu
    • Categories Dynamic Programming, Linear, Cone and Semidefinite Programming, Robust Optimization Tags , , , , ,

    We study two-stage adjustable robust linear programming in which the right-hand sides are uncertain and belong to a convex, compact uncertainty set. This problem is NP-hard, and the affine policy is a popular, tractable approximation. We prove that under standard and simple conditions, the two-stage problem can be reformulated as a copositive optimization problem, which … Read more

    Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls

  • Grani A. Hanasusanto
  • Daniel Kuhn
    • Categories Robust Optimization Tags , , ,

    Adaptive robust optimization problems are usually solved approximately by restricting the adaptive decisions to simple parametric decision rules. However, the corresponding approximation error can be substantial. In this paper we show that two-stage robust and distributionally robust linear programs can often be reformulated exactly as conic programs that scale polynomially with the problem dimensions. Specifically, … Read more

    On deterministic reformulations of distributionally robust joint chance constrained optimization problems

  • Shabbir Ahmed
  • Weijun Xie
    • Categories Convex Optimization, Robust Optimization, Stochastic Programming Tags , , ,

    A joint chance constrained optimization problem involves multiple uncertain constraints, i.e., constraints with stochastic parameters, that are jointly required to be satisfied with probability exceeding a prespecified threshold. In a distributionally robust joint chance constrained optimization problem (DRCCP), the joint chance constraint is required to hold for all probability distributions of the stochastic parameters from … Read more

    Quadratic Two-Stage Stochastic Optimization with Coherent Measures of Risk

  • Rodrigues Brian
  • Lizhi Liao
  • Jie Sun
    • Categories Linear, Cone and Semidefinite Programming, Robust Optimization, Stochastic Programming

    A new scheme to cope with two-stage stochastic optimization problems uses a risk measure as the objective function of the recourse action, where the risk measure is defined as the worst-case expected values over a set of constrained distributions. This paper develops an approach to deal with the case where both the first and second … Read more

    Ambiguous Risk Constraints with Moment and Unimodality Information

  • Ruiwei Jiang
  • Bowen Li
  • Johanna L. Mathieu
    • Categories Robust Optimization, Stochastic Programming Tags , , , , ,

    Optimization problems face random constraint violations when uncertainty arises in constraint parameters. Effective ways of controlling such violations include risk constraints, e.g., chance constraints and conditional Value-at-Risk (CVaR) constraints. This paper studies these two types of risk constraints when the probability distribution of the uncertain parameters is ambiguous. In particular, we assume that the distributional … Read more

    Closed-form solutions for worst-case law invariant risk measures with application to robust portfolio optimization

  • Jonathan Yu-Meng Li
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags ,

    Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), it is now known that their worst-case counterparts can be evaluated in closed form when only the first … Read more

    Stochastic and robust optimal operation of energy-efficient building with combined heat and power systems

  • Ping Liu
    • Categories Applications - Science and Engineering, Robust Optimization, Stochastic Programming Tags , ,

    Energy efficiency and renewable energy become more attractive in smart grid. In order to efficiently reduce global energy usage in building energy systems and to improve local environmental sustainability, it is essential to optimize the operation and the performance of combined heat and power (CHP) systems. In addition, intermittent renewable energy and imprecisely predicted customer … Read more

    Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets

  • Melvyn Sim
  • Huan Xu
  • Zhi Chen
    • Categories Robust Optimization Tags ,

    We consider a distributionally robust optimization problem where the ambiguity set of probability distributions is characterized by a tractable conic representable support set and expectation constraints. Specifically, we propose and motivate a new class of infinitely constrained ambiguity sets in which the number of expectation constraints could potentially be infinite. We show how the infinitely … Read more