Stochastic Programming

Stochastic Compositional Gradient Descent: Algorithms for Minimizing Compositions of Expected-Value Functions

  • Ethan Fang
  • Mengdi Wang
  • Han Liu
    • Categories Convex Optimization, Statistics, Stochastic Programming Tags , , , ,

    Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value functions, i.e., problems of the form $\min_x \E_v\[f_v\big(\E_w [g_w(x)]\big) \]$. In order to solve this stochastic composition problem, we propose a class … Read more

    A NEW PARTIAL SAMPLE AVERAGE APPROXIMATION METHOD FOR CHANCE CONSTRAINED PROBLEM

  • Jianqiang Cheng
  • Abdel Lisser
  • Céline Gicquel
    • Categories Stochastic Programming Tags , ,

    In this paper, we present a new scheme of a sampling method to solve chance constrained programs. First of all, a modified sample average approximation, namely Partial Sample Average Approximation (PSAA) is presented. The main advantage of our approach is that the PSAA problem has only continuous variables whilst the standard sample average approximation (SAA) … Read more

    Totally Unimodular Multistage Stochastic Programs

  • Andrew J. Schaefer
  • Oleg V. Shylo
  • Ruichen (Richard) Sun
    • Categories Stochastic Programming

    We consider totally unimodular multistage stochastic programs, that is, multistage stochastic programs whose extensive-form constraint matrices are totally unimodular. We establish several sufficient conditions and identify examples that have arisen in the literature. CitationRuichen (Richard) Sun, Oleg V. Shylo, Andrew J. Schaefer, Totally unimodular multistage stochastic programs, Operations Research Letters, Volume 43, Issue 1, January … Read more

    Rectangular sets of probability measures

  • Alexander Shapiro
    • Categories Stochastic Programming Tags , , , , , ,

    In this paper we consider the notion of rectangularity of a set of probability measures, introduced in Epstein and Schneider (2003), from a somewhat different point of view. We define rectangularity as a property of dynamic decomposition of a distributionally robust stochastic optimization problem and show how it relates to the modern theory of coherent … Read more

    Sequential Bounding Methods for Two-Stage Stochastic Programs

  • Brian T. Denton
  • Alexander Gose
    • Categories Production and Logistics, Stochastic Programming

    CitationAlexander H. Gose Graduate Program of Operations Research, North Carolina State University, Raleigh, NC 27695, ahgose@ncsu.edu Brian T. Denton Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI 48109, btdenton@umich.edu October 17, 2014 (Accepted for publication to INFORMS Journal on Computing)

    An Inertia-Free Filter Line-Search Algorithm for Large-Scale Nonlinear Programming

  • Naiyuan Chiang
  • Victor M. Zavala
    • Categories Nonlinear Optimization, Optimization of Systems modeled by PDEs, Stochastic Programming Tags , , , ,

    We present a filter line-search algorithm that does not require inertia information about the linear system to ensure global convergence. The proposed approach performs curvature tests along the search step to ensure descent. This feature permits more modularity in the linear algebra, enabling the use of a wider range of iterative and decomposition strategies. We … Read more

    Scenario-Tree Decomposition: Bounds for Multistage Stochastic Mixed-Integer Programs

  • Oleg A. Prokopyev
  • Andrew J. Schaefer
  • Gabriel L. Zenarosa
    • Categories Integer Programming, Parallel Algorithms, Stochastic Programming Tags , ,

    Multistage stochastic mixed-integer programming is a powerful modeling paradigm appropriate for many problems involving a sequence of discrete decisions under uncertainty; however, they are difficult to solve without exploiting special structures. We present scenario-tree decomposition to establish bounds for unstructured multistage stochastic mixed-integer programs. Our method decomposes the scenario tree into a number of smaller … Read more

    Information Relaxation Bounds for Infinite Horizon Markov Decision Processes

  • David B. Brown
  • Martin Haugh
    • Categories Dynamic Programming, Scheduling, Stochastic Programming Tags , ,

    We consider the information relaxation approach for calculating performance bounds for stochastic dynamic programs (DPs), following Brown, Smith, and Sun (2010). This approach generates performance bounds by solving problems with relaxed nonanticipativity constraints and a penalty that punishes violations of these constraints. In this paper, we study infinite horizon DPs with discounted costs and consider … Read more

    Dynamic Generation of Scenario Trees

  • Georg Ch. Pflug
  • Alois Pichler
    • Categories Stochastic Programming Tags , ,

    We present new algorithms for the dynamic generation of scenario trees for multistage stochastic optimization. The different methods described are based on random vectors, which are drawn from conditional distributions given the past and on sample trajectories. The structure of the tree is not determined beforehand, but dynamically adapted to meet a distance criterion, which … Read more

    An SDP approach for multiperiod mixed 0–1 linear programming models with stochastic dominance constraints for risk management

  • Laureano F. Escudero
  • Dolores Romero Morales
  • Juan F. Monge
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming, Supply Chain Management

    In this paper we consider multiperiod mixed 0–1 linear programming models under uncertainty. We propose a risk averse strategy using stochastic dominance constraints (SDC) induced by mixed-integer linear recourse as the risk measure. The SDC strategy extends the existing literature to the multistage case and includes both first-order and second-order constraints. We propose a stochastic … Read more