adjustable robust optimization

Decision-making with Side Information: A Causal Transport Robust Approach

  • Rui Gao
    • Categories Optimization in Data Science, Robust Optimization, Stochastic Programming Tags , , ,

    We consider stochastic optimization with side information where, prior to decision making, covariate data are available to inform better decisions. In particular, we propose to consider a distributionally robust formulation based on causal transport distance. Compared with divergence and Wasserstein metric, the causal transport distance is better at capturing the information structure revealed from the conditional distribution … Read more

    Robust Two-Stage Optimization with Covariate Data

  • Bart Paul Gerard Van Parys
  • Amine Bennouna
    • Categories Convex Optimization, Robust Optimization, Stochastic Programming Tags , ,

    We consider a generalization of two-stage decision problems in which the second-stage decision may be a function of a predictive signal but cannot adapt fully to the realized uncertainty. We will show how such problems can be learned from sample data by considering a family of regularized sample average formulations. Furthermore, our regularized data-driven formulations … Read more

    A New Dual-Based Cutting Plane Algorithm for Nonlinear Adjustable Robust Optimization

  • Abbas Khademi
  • Ahmadreza Marandi
  • Majid Soleimani-damaneh
    • Categories Robust Optimization Tags , , , , ,

    This paper explores a class of nonlinear Adjustable Robust Optimization (ARO) problems, containing here-and-now and wait-and-see variables, with uncertainty in the objective function and constraints. By applying Fenchel’s duality on the wait-and-see variables, we obtain an equivalent dual reformulation, which is a nonlinear static robust optimization problem. Using the dual formulation, we provide conditions under … Read more

    Optimal Robust Policy for Feature-Based Newsvendor

  • Luhao Zhang
  • Jincheng Yang
  • Rui Gao
    • Categories Infinite Dimensional Optimization, Robust Optimization, Supply Chain Management Tags , , ,

    We study policy optimization for the feature-based newsvendor, which seeks an end-to-end policy that renders an explicit mapping from features to ordering decisions. Unlike existing works that restrict the policies to some parametric class which may suffer from sub-optimality (such as affine class) or lack of interpretability (such as neural networks), we aim to optimize … Read more

    Adjustability in Robust Linear Optimization

  • Ningji Wei
  • Peter Yun Zhang
    • Categories Robust Optimization Tags , ,

    We investigate the concept of adjustability — the difference in objective values between two types of dynamic robust optimization formulations: one where (static) decisions are made before uncertainty realization, and one where uncertainty is resolved before (adjustable) decisions. This difference reflects the value of information and decision timing in optimization under uncertainty, and is related … 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

    Adjustable robust treatment-length optimization in radiation therapy

  • Ali Ajdari
  • Thomas Bortfeld
  • Dick den Hertog
  • Stefan ten Eikelder
    • Categories Biomedical Applications, Robust Optimization Tags , ,

    Traditionally, optimization of radiation therapy (RT) treatment plans has been done before the initiation of RT course, using population-wide estimates for patients’ response to therapy. However, recent technological advancements have enabled monitoring individual patient response during the RT course, in the form of biomarkers. Although biomarker data remains subject to substantial uncertainties, information extracted from … Read more

    Dual approach for two-stage robust nonlinear optimization

  • Frans J.C.T. de Ruiter
  • Dick den Hertog
  • Jianzhe Zhen
    • Categories Robust Optimization Tags , , ,

    Adjustable robust minimization problems in which the adjustable variables appear in a convex way are difficult to solve. For example, if we substitute linear decision rules for the adjustable variables, then the model becomes convex in the uncertain parameters, whereas for computational tractability we need concavity in the uncertain parameters. In this paper we reformulate … Read more

    Robust optimization for models with uncertain SOC and SDP constraints

  • Frans J.C.T. de Ruiter
  • Dick den Hertog
  • Ernst Roos
  • Jianzhe Zhen
    • Categories Robust Optimization Tags , , , ,

    In this paper we consider uncertain second-order cone (SOC) and semidefinite programming (SDP) constraints with polyhedral uncertainty, which are in general computationally intractable. We propose to reformulate an uncertain SOC or SDP constraint as a set of adjustable robust linear optimization constraints with an ellipsoidal or semidefinite representable uncertainty set, respectively. The resulting adjustable problem … Read more