Robust Optimization

Recycling Valid Inequalities for Robust Combinatorial Optimization with Budget Uncertainty

  • Christina Büsing
  • Timo Gersing
  • Arie M.C.A. Koster
    • Categories 0-1 Programming, Polyhedra, Robust Optimization Tags , , , ,

    Robust combinatorial optimization with budget uncertainty is one of the most popular approaches for integrating uncertainty into optimization problems. The existence of a compact reformulation for (mixed-integer) linear programs and positive complexity results give the impression that these problems are relatively easy to solve. However, the practical performance of the reformulation is quite poor when … Read more

    Connections between Robust and Bilevel Optimization

  • Marc Goerigk
  • Jannis Kurtz
  • Martin Schmidt
  • Johannes Thürauf
    • Categories Robust Optimization Tags , ,

    Robust and bilevel optimization share the common feature that they involve a certain multilevel structure. Hence, although they model something rather different when used in practice, they seem to have a similar mathematical structure. In this paper, we analyze the connections between different types of robust problems (static robust problems with and without decision-dependence of … Read more

    Distributionally Risk-Receptive and Robust Multistage Stochastic Integer Programs and Interdiction Models

  • Sumin Kang
  • Manish Bansal
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization, Stochastic Programming Tags , , , , , ,

    In this paper, we study distributionally risk-receptive and distributionally robust (or risk-averse) multistage stochastic mixed-integer programs (denoted by DRR- and DRO-MSIPs). We present cutting plane-based and reformulation-based approaches for solving DRR- and DRO-MSIPs without and with decision-dependent uncertainty to optimality. We show that these approaches are finitely convergent with probability one. Furthermore, we introduce generalizations … Read more

    Randomized Robust Price Optimization

  • Xinyi Guan
  • Velibor Mišić
    • Categories Applications - OR and Management Sciences, Linear, Cone and Semidefinite Programming, Robust Optimization Tags , ,

    The robust multi-product pricing problem is to determine the prices of a collection of products so as to maximize the worst-case revenue, where the worst case is taken over an uncertainty set of demand models that the firm expects could be realized in practice. A tacit assumption in this approach is that the pricing decision … Read more

    Mixed-Integer Programming for a Class of Robust Submodular Maximization Problems

  • Hsin-Yi Huang
  • Hao-Hsiang Wu
  • Simge Küçükyavuz
    • Categories (Mixed) Integer Linear Programming, Robust Optimization, Stochastic Programming

    We consider robust submodular maximization problems (RSMs), where given a set of \(m\) monotone submodular objective functions, the robustness is with respect to the worst-case (scaled) objective function. The model we consider generalizes two variants of robust submodular maximization problems in the literature, depending on the choice of the scaling vector. On one hand, by using … Read more

    Nonlinear Distributionally Robust Optimization

  • Rayyan
  • Peyman Mohajerin Esfahani
    • Categories Infinite Dimensional Optimization, Optimization in Data Science, Robust Optimization Tags , ,

    This article focuses on a class of distributionally robust optimization (DRO) problems where, unlike the growing body of the literature, the objective function is potentially non-linear in the distribution. Existing methods to optimize nonlinear functions in probability space use the Frechet derivatives, which present both theoretical and computational challenges. Motivated by this, we propose an … Read more

    Distributionally Robust Linear Quadratic Control

  • Bahar Tașkesen
  • Dan Iancu
  • Çağıl Koçyiğit
  • Daniel Kuhn
    • Categories Control Applications, Dynamic Programming, Robust Optimization

    Linear-Quadratic-Gaussian (LQG) control is a fundamental control paradigm that is studied in various fields such as engineering, computer science, economics, and neuroscience. It involves controlling a system with linear dynamics and imperfect observations, subject to additive noise, with the goal of minimizing a quadratic cost function for the state and control variables. In this work, … Read more

    Safely Learning Dynamical Systems

  • Abraar Chaudhry
  • Amir Ali Ahmadi
  • Vikas Sindhwani
  • Stephen Tu
    • Categories Control Applications, Linear, Cone and Semidefinite Programming, Robust Optimization Tags , , , ,

    A fundamental challenge in learning an unknown dynamical system is to reduce model uncertainty by making measurements while maintaining safety. In this work, we formulate a mathematical definition of what it means to safely learn a dynamical system by sequentially deciding where to initialize the next trajectory. In our framework, the state of the system … Read more

    A Moment-SOS Hierarchy for Robust Polynomial Matrix Inequality Optimization with SOS-Convexity

  • Jie Wang
  • Feng Guo
    • Categories Global Optimization Applications, Robust Optimization, Semi-definite Programming Tags , , , ,

    We study a class of polynomial optimization problems with a robust polynomial matrix inequality constraint for which the uncertainty set is defined also by a polynomial matrix inequality (including robust polynomial semidefinite programs as a special case). Under certain SOS-convexity assumptions, we construct a hierarchy of moment-SOS relaxations for this problem to obtain convergent upper … Read more

    Robust optimal design of a tree-based water distribution network with intermittent demand

  • Frédéric Babonneau
  • Jean-Philippe Vial
    • Categories Robust Optimization Tags , , ,

    This paper discusses the design of a tree-shaped water distribution system for small, dispersed rural communities. It revisits the topic that was discussed in [Babonneau et al., 2019] and is nowadays implemented in the field. It proposes a new approach to pipe selection based on robust optimization to account for the uncertainty inherent in intermittent … Read more