Stochastic Programming

Mitigating Uncertainty via Compromise Decisions in Two-stage Stochastic Linear Programming

  • Suvrajeet Sen
  • Yifan Liu
    • Categories Stochastic Programming Tags , ,

    Stochastic Programming (SP) has long been considered as a well-justified yet computationally challenging paradigm for practical applications. Computational studies in the literature often involve approximating a large number of scenarios by using a small number of scenarios to be processed via deterministic solvers, or running Sample Average Approximation on some genre of high performance machines … Read more

    Confidence Levels for CVaR Risk Measures and Minimax Limits

  • Edward Anderson
  • Huifu Xu
  • Dali Zhang
    • Categories Robust Optimization, Semi-infinite Programming, Stochastic Programming

    Conditional value at risk (CVaR) has been widely used as a risk measure in finance. When the confidence level of CVaR is set close to 1, the CVaR risk measure approximates the extreme (worst scenario) risk measure. In this paper, we present a quantitative analysis of the relationship between the two risk measures and its … Read more

    A Two-Stage Stochastic Integer Programming Approach to Integrated Staffing and Scheduling with Application to Nurse Management

  • Kibaek Kim
  • Sanjay Mehrotra
    • Categories (Mixed) Integer Nonlinear Programming, Scheduling, Stochastic Programming Tags , , , , ,

    We study the problem of integrated staffing and scheduling under demand uncertainty. The problem is formulated as a two-stage stochastic integer program with mixed-integer recourse. The here-and-now decision is to find initial staffing levels and schedules, well ahead in time. The wait-and-see decision is to adjust these schedules at a time epoch closer to the … Read more

    Generalized Gauss Inequalities via Semidefinite Programming

  • Paul J. Goulart
  • Daniel Kuhn
  • Bart Paul Gerard Van Parys
    • Categories Convex Optimization, Statistics, Stochastic Programming Tags , ,

    A sharp upper bound on the probability of a random vector falling outside a polytope, based solely on the first and second moments of its distribution, can be computed efficiently using semidefinite programming. However, this Chebyshev-type bound tends to be overly conservative since it is determined by a discrete worst-case distribution. In this paper we … Read more

    Benders, Nested Benders and Stochastic Programming: An Intuitive Introduction

  • James Murphy
    • Categories Stochastic Programming Tags , , , , , , ,

    This article aims to explain the Nested Benders algorithm for the solution of large-scale stochastic programming problems in a way that is intelligible to someone coming to it for the first time. In doing so it gives an explanation of Benders decomposition and of its application to two-stage stochastic programming problems (also known in this … Read more

    Penalty Methods with Stochastic Approximation for Stochastic Nonlinear Programming

  • Shiqian Ma
  • Xiao Wang
  • Ya-xiang Yuan
    • Categories Nonlinear Optimization, Stochastic Programming

    In this paper, we propose a class of penalty methods with stochastic approximation for solving stochastic nonlinear programming problems. We assume that only noisy gradients or function values of the objective function are available via calls to a stochastic first-order or zeroth-order oracle. In each iteration of the proposed methods, we minimize an exact penalty … Read more

    Reactive Power Management using Firefly and Spiral Optimization under Static and Dynamic Loading Conditions

  • Ripunjoy Phukan
    • Categories Applications - Science and Engineering, Global Optimization Applications, Stochastic Programming Tags , , , ,

    Power System planning encompasses the concept of minimization of transmission losses keeping in mind the voltage stability and system reliability. Voltage profile decides the state of a system and its control is dependent on Generator source voltage, shunt/series injection, transformer taps etc. Optimal parameter setting in system level is needed for managing the available resources … Read more

    Decision Making Based on a Nonparametric Shape-Preserving Perturbation of a Reference Utility Function

  • Jian Hu
    • Categories Finance and Economics, Robust Optimization, Stochastic Programming Tags , , , ,

    This paper develops a robust optimization based decision-making framework using a nonparametric perturbation of a reference utility function. The perturbation preserves the risk-aversion property but solves the problem of ambiguity and inconsistency in eliciting the reference utility function. We study the topology of the perturbation, and show that in the decision-making framework the price of … Read more

    Computation of Stochastic Nash Equilibrium via Variable Sample Distributed Methods

  • Ming Dong
  • Lizhi Wang
  • Dali Zhang
    • Categories Game Theory, Stochastic Programming Tags

    In this paper, we propose a variable sample distributed algorithm for the computation of stochastic Nash equilibrium in which the objective functions are replaced, at each iteration, by sample average approximations. We investigate the contraction mapping properties of the variable sample distributed algorithm and show that the accuracy of estimators yielded in the algorithms to … Read more

    Robust Data-Driven Dynamic Programming

  • Grani A. Hanasusanto
  • Daniel Kuhn
    • Categories Dynamic Programming, Robust Optimization, Stochastic Programming Tags , , ,

    In stochastic optimal control the distribution of the exogenous noise is typically unknown and must be inferred from limited data before dynamic programming (DP)-based solution schemes can be applied. If the conditional expectations in the DP recursions are estimated via kernel regression, however, the historical sample paths enter the solution procedure directly as they determine … Read more