Robust Optimization

Finite-Sample Guarantees for Wasserstein Distributionally Robust Optimization: Breaking the Curse of Dimensionality

  • Rui Gao
    • Categories Robust Optimization, Statistics, Stochastic Programming Tags , , , ,

    Wasserstein distributionally robust optimization (DRO) aims to find robust and generalizable solutions by hedging against data perturbations in Wasserstein distance. Despite its recent empirical success in operations research and machine learning, existing performance guarantees for generic loss functions are either overly conservative due to the curse of dimensionality, or plausible only in large sample asymptotics. … Read more

    Randomized Assortment Optimization

  • Zhengchao Wang
  • Heikki Peura
  • Wolfram Wiesemann
    • Categories Robust Optimization, Yield Management

    When a firm selects an assortment of products to offer to customers, it uses a choice model to anticipate their probability of purchasing each product. In practice, the estimation of these models is subject to statistical errors, which may lead to significantly suboptimal assortment decisions. Recent work has addressed this issue using robust optimization, where … Read more

    Robust Convex Optimization: A New Perspective That Unifies And Extends

  • Dimitris Bertsimas
  • Dick den Hertog
  • Jean Pauphilet
  • Jianzhe Zhen
    • Categories Convex Optimization, Robust Optimization Tags , , ,

    Robust convex constraints are difficult to handle, since finding the worst-case scenario is equivalent to maximizing a convex function. In this paper, we propose a new approach to deal with such constraints that unifies approaches known in the literature and extends them in a significant way. The extension is either obtaining better solutions than the … Read more

    Global Optimization for the Multilevel European Gas Market System with Nonlinear Flow Models on Trees

  • Lars Schewe
  • Martin Schmidt
  • Johannes Thürauf
    • Categories Applications - OR and Management Sciences, Global Optimization, Robust Optimization Tags , , , ,

    The European gas market is implemented as an entry-exit system, which aims to decouple transport and trading of gas. It has been modeled in the literature as a multilevel problem, which contains a nonlinear flow model of gas physics. Besides the multilevel structure and the nonlinear flow model, the computation of so-called technical capacities is … Read more

    Affinely Adjustable Robust Linear Complementarity Problems

  • Christian Biefel
  • Frauke Liers
  • Martin Schmidt
  • Jan Hendrik Rolfes
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities, Robust Optimization Tags , , , ,

    Linear complementarity problems are a powerful tool for modeling many practically relevant situations such as market equilibria. They also connect many sub-areas of mathematics like game theory, optimization, and matrix theory. Despite their close relation to optimization, the protection of LCPs against uncertainties – especially in the sense of robust optimization – is still in … Read more

    Statistical Robustness in Utility Preference Robust Optimization Models

  • Shaoyan Guo
  • Huifu Xu
    • Categories Robust Optimization Tags , , ,

    Utility preference robust optimization (PRO) concerns decision making problems where information on decision maker’s utility preference is incomplete and has to be elicited through partial information and the optimal decision is based on the worst case utility function elicited. A key assumption in the PRO models is that the true probability distribution is either known … Read more

    Strong Formulations for Distributionally Robust Chance-Constrained Programs with Left-Hand Side Uncertainty under Wasserstein Ambiguity

  • Nam Ho-Nguyen
  • Fatma Kılınç-Karzan
  • Simge Küçükyavuz
  • Dabeen Lee
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    Distributionally robust chance-constrained programs (DR-CCP) over Wasserstein ambiguity sets exhibit attractive out-of-sample performance and admit big-$M$-based mixed-integer programming (MIP) reformulations with conic constraints. However, the resulting formulations often suffer from scalability issues as sample size increases. To address this shortcoming, we derive stronger formulations that scale well with respect to the sample size. Our focus … Read more

    An Integer Programming Approach to Deep Neural Networks with Binary Activation Functions

  • Bubacarr Bah
  • Jannis Kurtz
    • Categories (Mixed) Integer Linear Programming, Other Topics, Robust Optimization Tags , , ,

    We study deep neural networks with binary activation functions (BDNN), i.e. the activation function only has two states. We show that the BDNN can be reformulated as a mixed-integer linear program which can be solved to global optimality by classical integer programming solvers. Additionally, a heuristic solution algorithm is presented and we study the model … Read more

    Convex Maximization via Adjustable Robust Optimization

  • Aharon Ben-Tal
  • Ruud C.M. Brekelmans
  • Dick den Hertog
  • Aras Selvi
    • Categories Global Optimization, Nonlinear Optimization, Robust Optimization Tags , ,

    Maximizing a convex function over convex constraints is an NP-hard problem in general. We prove that such a problem can be reformulated as an adjustable robust optimization (ARO) problem where each adjustable variable corresponds to a unique constraint of the original problem. We use ARO techniques to obtain approximate solutions to the convex maximization problem. … Read more

    A Unified Framework for Adjustable Robust Optimization with Endogenous Uncertainty

  • Wei Feng
  • Qi Zhang
    • Categories Robust Optimization Tags , ,

    This work proposes a framework for multistage adjustable robust optimization that unifies the treatment of three different types of endogenous uncertainty, where decisions, respectively, (i) alter the uncertainty set, (ii) affect the materialization of uncertain parameters, and (iii) determine the time when the true values of uncertain parameters are observed. We provide a systematic analysis … Read more