Wolfram Wiesemann

K-Adaptability in Two-Stage Distributionally Robust Binary Programming

  • Grani A. Hanasusanto
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Integer Programming, Robust Optimization

    We propose to approximate two-stage distributionally robust programs with binary recourse decisions by their associated K-adaptability problems, which pre-select K candidate second-stage policies here-and-now and implement the best of these policies once the uncertain parameters have been observed. We analyze the approximation quality and the computational complexity of the K-adaptability problem, and we derive explicit … Read more

    A Comment on “Computational Complexity of Stochastic Programming Problems”

  • Grani A. Hanasusanto
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Stochastic Programming

    Although stochastic programming problems were always believed to be computationally challenging, this perception has only recently received a theoretical justification by the seminal work of Dyer and Stougie (Mathematical Programming A, 106(3):423–432, 2006). Amongst others, that paper argues that linear two-stage stochastic programs with fixed recourse are #P-hard even if the random problem data is … Read more

    Robust Growth-Optimal Portfolios

  • Daniel Kuhn
  • Napat Rujeerapaiboon
  • Wolfram Wiesemann
    • Categories Robust Optimization, Stochastic Programming Tags ,

    The growth-optimal portfolio is designed to have maximum expected log-return over the next rebalancing period. Thus, it can be computed with relative ease by solving a static optimization problem. The growth-optimal portfolio has sparked fascination among finance professionals and researchers because it can be shown to outperform any other portfolio with probability 1 in the … Read more

    K-Adaptability in Two-Stage Robust Binary Programming

  • Grani A. Hanasusanto
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Integer Programming, Robust Optimization Tags , ,

    Over the last two decades, robust optimization has emerged as a computationally attractive approach to formulate and solve single-stage decision problems affected by uncertainty. More recently, robust optimization has been successfully applied to multi-stage problems with continuous recourse. This paper takes a step towards extending the robust optimization methodology to problems with integer recourse, which … 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

    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

    Pessimistic Bi-Level Optimisation

  • Polyxeni-Margarita Kleniati
  • Berc Rustem
  • Angelos Tsoukalas
  • Wolfram Wiesemann
    • Categories Global Optimization Theory

    Bi-level problems are optimisation problems in which some of the decision variables must optimise a subordinate (lower-level) problem. In general, the lower-level problem can possess multiple optimal solutions. One therefore distinguishes between optimistic formulations, which assume that the most favourable lower-level solution is implemented, and pessimistic formulations, in which the most adverse lower-level solution is … Read more

    The Decision Rule Approach to Optimization under Uncertainty: Methodology and Applications

  • Angelos Georghiou
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , ,

    Dynamic decision-making under uncertainty has a long and distinguished history in operations research. Due to the curse of dimensionality, solution schemes that naively partition or discretize the support of the random problem parameters are limited to small and medium-sized problems, or they require restrictive modeling assumptions (e.g., absence of recourse actions). In the last few … Read more

    Generalized Decision Rule Approximations for Stochastic Programming via Liftings

  • Angelos Georghiou
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Robust Optimization Tags , , ,

    Stochastic programming provides a versatile framework for decision-making under uncertainty, but the resulting optimization problems can be computationally demanding. It has recently been shown that, primal and dual linear decision rule approximations can yield tractable upper and lower bounds on the optimal value of a stochastic program. Unfortunately, linear decision rules often provide crude approximations … Read more

    Robust Markov Decision Processes

  • Daniel Kuhn
  • Berc Rustem
  • Wolfram Wiesemann
    • Categories Dynamic Programming, Robust Optimization

    Markov decision processes (MDPs) are powerful tools for decision making in uncertain dynamic environments. However, the solutions of MDPs are of limited practical use due to their sensitivity to distributional model parameters, which are typically unknown and have to be estimated by the decision maker. To counter the detrimental effects of estimation errors, we consider … Read more