stochastic programming

A Framework for Solving Chance-Constrained Linear Matrix Inequality Programs

  • Jianqiang Cheng
  • Miguel A. Lejeune
  • Roya Karimi
    • Categories Stochastic Programming Tags , , , ,

    We propose a novel partial sample average approximation (PSAA) framework to solve the two main types of chance-constrained linear matrix inequality (CCLMI) problems: CCLMI with random technology matrix, and CCLMI with random right-hand side. We propose a series of computationally tractable PSAA-based approximations for CCLMI problems, analyze their properties, and derive sufficient conditions ensuring convexity. … Read more

    Two-stage Stochastic Programming with Linearly Bi-parameterized Quadratic Recourse

  • Ying Cui
  • Junyi Liu
  • Jong-Shi Pang
  • Suvrajeet Sen
    • Categories Stochastic Programming Tags , ,

    This paper studies the class of two-stage stochastic programs (SP) with a linearly bi-parameterized recourse function defined by a convex quadratic program. A distinguishing feature of this new class of stochastic programs is that the objective function in the second stage is linearly parameterized by the first-stage decision variable, in addition to the standard linear … Read more

    Reinforcement Learning via Parametric Cost Function Approximation for Multistage Stochastic Programming

  • Saeed Ghadimi
  • Raymond Perkins
  • Warren B. Powell
    • Categories Applications - OR and Management Sciences, Optimization of Simulated Systems, Stochastic Programming Tags , , , ,

    The most common approaches for solving stochastic resource allocation problems in the research literature is to either use value functions (“dynamic programming”) or scenario trees (“stochastic programming”) to approximate the impact of a decision now on the future. By contrast, common industry practice is to use a deterministic approximation of the future which is easier … Read more

    Machine learning approach to chance-constrained problems: An algorithm based on the stochastic gradient descent

  • Lukáš Adam
  • Martin Branda
    • Categories Stochastic Programming Tags , , , , ,

    We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the decision variable based only on looking at a few scenarios. We modify it to handle the non-separable objective. A complexity … Read more

    Decomposition Methods for Solving Markov Decision Processes with Multiple Models of the Parameters

  • Vinayak Ahluwalia
  • Brian T. Denton
  • Charmee Kamdar
  • Lauren Steimle
    • Categories Dynamic Programming, Stochastic Programming Tags , , , ,

    We consider the problem of decision-making in Markov decision processes (MDPs) when the reward or transition probability parameters are not known with certainty. We consider an approach in which the decision-maker (DM) considers multiple models of the parameters for an MDP and wishes to find a policy that optimizes an objective function that considers the … Read more

    Multi-component Maintenance Optimization: A Stochastic Programming Approach

  • Yisha Xiang
  • Bo Zeng
  • Zhicheng Zhu
    • Categories Applications - OR and Management Sciences, Stochastic Programming Tags , , , ,

    Maintenance optimization has been extensively studied in the past decades. However, most of the existing maintenance models focus on single-component systems. Multi-component maintenance optimization, which joins the stochastic failure processes with the combinatorial maintenance grouping problems, remains as an open issue. To address this challenge, we study this problem in a finite planning horizon by … Read more

    The policy graph decomposition of multistage stochastic optimization problems

  • Oscar Dowson
    • Categories Stochastic Programming Tags , , ,

    We propose the policy graph as a way of formulating multistage stochastic optimization problems. We also propose an extension to the stochastic dual dynamic programming algorithm to solve a class of problems formulated as a policy graph. This class includes discrete-time, infinite horizon, multistage stochastic optimization problems with continuous state and control variables. ArticleDownload View … Read more

    Projective Hedging for Stochastic Programming

  • Jonathan Eckstein
  • Jean-Paul Watson
  • David L. Woodruff
    • Categories Convex Optimization, Stochastic Programming Tags , , ,

    We propose a decomposition algorithm for multistage stochastic programming that resembles the progressive hedging method of Rockafellar and Wets, but is provably capable of several forms of asynchronous operation. We derive the method from a class of projective operator splitting methods fairly recently proposed by Combettes and Eckstein, significantly expanding the known applications of those … Read more

    Bounds for Probabilistic Programming with Application to a Blend Planning Problem

  • Abdel Lisser
  • Francesca Maggioni
  • Shen Peng
    • Categories Stochastic Programming Tags , , , , ,

    In this paper, we derive deterministic inner approximations for single and joint probabilistic constraints based on classical inequalities from probability theory such as the one-sided Chebyshev inequality, Bernstein inequality, Chernoff inequality and Hoeffding inequality (see Pinter 1989). New assumptions under which the bounds based approximations are convex allowing to solve the problem efficiently are derived. … Read more

    Inexact cutting planes for two-stage mixed-integer stochastic programs

  • Ward Romeijnders
  • Niels van der Laan
    • Categories Cutting Plane Approaches, Stochastic Programming Tags , , ,

    We propose a novel way of applying cutting plane techniques to two-stage mixed-integer stochastic programs. Instead of using cutting planes that are always valid, our idea is to apply inexact cutting planes to the second-stage feasible regions that may cut away feasible integer second-stage solutions for some scenarios and may be overly conservative for others. … Read more