Robust Optimization

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

    Reliable p-median facility location problem: two-stage robust models and algorithms

  • Yu An
  • Bo Zeng
  • Yu Zhang
  • Long Zhao
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , , ,

    In this paper, we propose a set of two-stage robust optimization models to design reliable p-median facility location networks subject to disruptions. A customized column-and- constraint generation approach is implemented and shown to be more effective than Benders cutting plane method. Numerical experiments are performed on real data and management insights on system design are … 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

    Kullback-Leibler Divergence Constrained Distributionally Robust Optimization

  • Jeff L Hong
  • Zhaolin Hu
    • Categories Nonlinear Optimization, Robust Optimization, Stochastic Programming

    In this paper we study distributionally robust optimization (DRO) problems where the ambiguity set of the probability distribution is defined by the Kullback-Leibler (KL) divergence. We consider DRO problems where the ambiguity is in the objective function, which takes a form of an expectation, and show that the resulted minimax DRO problems can be formulated … Read more

    Worst-case-expectation approach to optimization under uncertainty

  • Joari Paulo da Costa
  • Alexander Shapiro
  • Murilo Pereira Soares
  • Wajdi Tekaya
    • Categories Applications - OR and Management Sciences, Robust Optimization, Stochastic Programming Tags , , , , , , , ,

    In this paper we discuss multistage programming with the data process subject to uncertainty. We consider a situation were the data process can be naturally separated into two components, one can be modeled as a random process, with a specified probability distribution, and the other one can be treated from a robust (worst case) point … Read more

    Deriving robust and globalized robust solutions of uncertain linear programs with general convex uncertainty sets

  • Aharon Ben-Tal
  • Dick den Hertog
  • Bram L. Gorissen
  • Hans Blanc
    • Categories Robust Optimization

    We propose a new way to derive tractable robust counterparts of a linear program by using the theory of Beck and Ben-Tal (2009) on the duality between the robust (“pessimistic”) primal problem and its “optimistic” dual. First, we obtain a new {\it convex} reformulation of the dual problem of a robust linear program, and then … Read more

    Robust combinatorial optimization with variable budgeted uncertainty

  • Michael Poss
    • Categories Robust Optimization

    We introduce a new model for robust combinatorial optimization where the uncertain parameters belong to the image of multifunctions of the problem variables. In particular, we study the variable budgeted uncertainty, an extension of the budgeted uncertainty introduced by Bertsimas and Sim. Variable budgeted uncertainty can provide the same probabilistic guarantee as the budgeted uncertainty … Read more

    Distributionally Robust Multi-Item Newsvendor Problems with Multimodal Demand Distributions

  • Grani A. Hanasusanto
  • Daniel Kuhn
  • Stein W. Wallace
  • Steve Zymler
    • Categories Robust Optimization

    We present a risk-averse multi-dimensional newsvendor model for a class of products whose demands are strongly correlated and subject to fashion trends that are not fully understood at the time when orders are placed. The demand distribution is known to be multimodal in the sense that there are spatially separated clusters of probability mass but … Read more

    The robust vehicle routing problem with time windows

  • Agostinho Agra
  • Michael Poss
  • Marielle Christiansen
  • Rosa Figueiredo
  • Lars M. Hvattum
  • Cristina Requejo
    • Categories Robust Optimization, Transportation

    This paper addresses the robust vehicle routing problem with time windows. We are motivated by a problem that arises in maritime transportation where delays are frequent and should be taken into account. Our model only allows routes that are feasible for all values of the travel times in a predetermined uncertainty polytope, which yields a … Read more