Robust Optimization

A General Wasserstein Framework for Data-driven Distributionally Robust Optimization: Tractability and Applications

  • Jonathan Yu-Meng Li
  • Tiantian Mao
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    Data-driven distributionally robust optimization is a recently emerging paradigm aimed at finding a solution that is driven by sample data but is protected against sampling errors. An increasingly popular approach, known as Wasserstein distributionally robust optimization (DRO), achieves this by applying the Wasserstein metric to construct a ball centred at the empirical distribution and finding … 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

    Robust Contextual Portfolio Optimization with Gaussian Mixture Models

  • Yijie Wang
  • Ling Dai
  • Grani A. Hanasusanto
  • Chin Pang Ho
    • Categories Finance and Economics, Robust Optimization Tags , ,

    We consider the portfolio optimization problem with contextual information that is available to better quantify and predict the uncertain returns of assets. Motivated by the regime modeling techniques for the finance market, we consider the setting where both the uncertain returns and the contextual information follow a Gaussian Mixture (GM) distribution. This problem is shown … Read more

    Hidden convexity in a class of optimization problems with bilinear terms

  • Bram L. Gorissen
  • Meike Reusken
  • Dick den Hertog
    • Categories Nonlinear Optimization, Robust Optimization Tags , , ,

    In this paper we identify a new class of nonconvex optimization problems that can be equivalently reformulated to convex ones. These nonconvex problems can be characterized by convex functions with bilinear arguments. We describe several examples of important applications that have this structure. These include the problems with variable coefficients, the dual of robust nonlinear … Read more

    Robust planning of production routing problem in closed-loop supply chain of beverage glass bottles

  • Ali Borumand
  • Ahmadreza Marandi
  • Ali Nookabadi
  • Zümbül Atan
    • Categories Robust Optimization, Stochastic Programming, Supply Chain Management Tags , , , ,

    Closed-loop supply chains (CLSC) integrate forward and reverse flows of products and information. This integration helps companies to manage their supply chains better as they have more control and a broader view of the whole chain. Also, companies can have economic and environmental benefits from the returned products. Despite these advantages, managing CLSCs can be … Read more

    A Survey on Bilevel Optimization Under Uncertainty

  • Yasmine Beck
  • Ivana Ljubić
  • Martin Schmidt
    • Categories Global Optimization, Robust Optimization, Stochastic Programming Tags , , ,

    Bilevel optimization is a very active field of applied mathematics. The main reason is that bilevel optimization problems can serve as a powerful tool for modeling hierarchical decision making processes. This ability, however, also makes the resulting problems challenging to solve—both in theory and practice. Fortunately, there have been significant algorithmic advances in the field … Read more

    Decision Rule Approaches for Pessimistic Bilevel Linear Programs under Moment Ambiguity with Facility Location Applications

  • Akshit Goyal
  • Yiling Zhang
  • Chuan He
    • Categories Robust Optimization, Semi-definite Programming Tags , , , ,

    We study a pessimistic stochastic bilevel program in the context of sequential two-player games, where the leader makes a binary here-and-now decision, and the follower responds a continuous wait-and-see decision after observing the leader’s action and revelation of uncertainty. Only the information of the mean, covariance, and support is known. We formulate the problem as … Read more

    The Analytics of Robust Satisficing: Predict, Optimize, Satisfice, then Fortify

  • Melvyn Sim
  • Qinshen Tang
  • Minglong Zhou
  • Taozeng Zhu
    • Categories Robust Optimization Tags , , ,

    We introduce a novel approach to prescriptive analytics that leverages robust satisficing techniques to determine optimal decisions in situations of risk ambiguity and prediction uncertainty. Our decision model relies on a reward function that incorporates uncertain parameters, which can be partially predicted using available side information. However, the accuracy of the linear prediction model depends … Read more

    On Approximations of Data-Driven Chance Constrained Programs over Wasserstein Balls

  • Zhi Chen
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Robust Optimization Tags , , , ,

    Distributionally robust chance constrained programs minimize a deterministic cost function subject to the satisfaction of one or more safety conditions with high probability, given that the probability distribution of the uncertain problem parameters affecting the safety condition(s) is only known to belong to some ambiguity set. We study two popular approximation schemes for distributionally robust … Read more

    Robust Optimization with Continuous Decision-Dependent Uncertainty with Applications in Demand Response Portfolio Management

  • Hongfan(Kevin) Chen
  • Xu Andy Sun
  • Haoxiang Yang
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , ,

    We consider a robust optimization problem with continuous decision-dependent uncertainty (RO-CDDU), which has two new features: an uncertainty set linearly dependent on continuous decision variables and a convex piecewise-linear objective function. We prove that RO-CDDU is strongly NP-hard in general and reformulate it into an equivalent mixed-integer nonlinear program (MINLP) with a decomposable structure to … Read more