robust optimization

A cutting surface algorithm for semi-infinite convex programming with an application to moment robust optimization

  • Sanjay Mehrotra
  • Dávid Papp
    • Categories Robust Optimization, Semi-infinite Programming, Stochastic Programming Tags , , , , , , ,

    We first present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop an algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. The cutting surface algorithm is also applicable to problems with non-differentiable semi-infinite … Read more

    Exploring the Modeling Capacity of Two-stage Robust Optimization — Two Variants of Robust Unit Commitment Model

  • Yu An
  • Bo Zeng
    • Categories Applications - Science and Engineering, Robust Optimization Tags , ,

    To handle significant variability in loads, renewable energy generation, as well as various contingencies, two-stage robust optimization method has been adopted to construct unit commitment models and to ensure reliable solutions. In this paper, we further explore and extend the modeling capacity of two-stage robust optimization and present two new robust unit commitment variants, the … Read more

    Interdiction Games on Markovian PERT Networks

  • Eli Gutin
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Stochastic Programming Tags , , ,

    In a stochastic interdiction game a proliferator aims to minimize the expected duration of a nuclear weapons development project, while an interdictor endeavors to maximize the project duration by delaying some of the project tasks. We formulate static and dynamic versions of the interdictor’s decision problem where the interdiction plan is either pre-committed or adapts … Read more

    2-Stage Robust MILP with continuous recourse variables

  • Alain Billionnet
  • Marie-Christine Costa
  • Pierre-Louis Poirion
    • Categories Combinatorial Optimization Tags ,

    We solve a linear robust problem with mixed-integer first-stage variables and continuous second stage variables. We consider column wise uncertainty. We first focus on a problem with right hand-side uncertainty which satisfies a “full recourse property” and a specific definition of the uncertainty. We propose a solution based on a generation constraint algorithm. Then we … Read more

    Robust combinatorial optimization with cost uncertainty

  • Michael Poss
    • Categories Combinatorial Optimization, Robust Optimization Tags , , , ,

    We present in this paper a new model for robust combinatorial optimization with cost uncertainty that generalizes the classical budgeted uncertainty set. We suppose here that the budget of uncertainty is given by a function of the problem variables, yielding an uncertainty multifunction. The new model is less conservative than the classical model and approximates … Read more

    Distributionally Robust Convex Optimization

  • Daniel Kuhn
  • Melvyn Sim
  • Wolfram Wiesemann
    • Categories Convex Optimization, Robust Optimization, Stochastic Programming Tags , ,

    Distributionally robust optimization is a paradigm for decision-making under uncertainty where the uncertain problem data is governed by a probability distribution that is itself subject to uncertainty. The distribution is then assumed to belong to an ambiguity set comprising all distributions that are compatible with the decision maker’s prior information. In this paper, we propose … Read more

    Robust Optimization under Multi-band Uncertainty – Part I: Theory

  • Christina Büsing
  • Fabio D'Andreagiovanni
    • Categories (Mixed) Integer Linear Programming, Polyhedra, Robust Optimization Tags , , , ,

    The classical single-band uncertainty model introduced by Bertsimas and Sim has represented a breakthrough in the development of tractable robust counterparts of Linear Programs. However, adopting a single deviation band may be too limitative in practice: in many real-world problems, observed deviations indeed present asymmetric distributions over asymmetric ranges, so that getting a higher modeling … Read more

    Robust Least Square Semidefinite Programming with Applications to Correlation Stress Testing

  • Guoyin Li
  • Ting Kei Pong
  • K.C. Ma
    • Categories Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming, Robust Optimization Tags , ,

    In this paper, we consider a least square semidefinite programming problem under ellipsoidal data uncertainty. We show that the robustification of this uncertain problem can be reformulated as a semidefinite linear programming problem with an additional second-order cone constraint. We then provide an explicit quantitative sensitivity analysis on how the solution under the robustification depends … Read more

    Robust Metric Inequalities for the Γ-Robust Network Loading Problem

  • Grit Claßen
  • Arie M.C.A. Koster
  • Manuel Kutschka
  • Issam Tahiri
    • Categories Network Optimization, Robust Optimization Tags , , ,

    In this paper, we consider the network loading problem under demand uncertainties with static routing, i.e, a single routing scheme based on the fraction of the demands has to be determined. We generalize the class of metric inequalities to the Γ-robust setting and show that they yield a formulation in the capacity space. We describe … Read more

    Exact Solution of the Robust Knapsack Problem

  • Michele Monaci
  • Ulrich Pferschy
  • Paolo Serafini
    • Categories Combinatorial Optimization, Dynamic Programming, Robust Optimization Tags , ,

    We consider an uncertain variant of the knapsack problem in which the weight of the items is not exactly known in advance, but belongs to a given interval, and an upper bound is imposed on the number of items whose weight di ffers from the expected one. For this problem, we provide a dynamic programming algorithm … Read more