stochastic programming

A Tractable Approximation of Stochastic Programming via Robust Optimization

  • Xin Chen
  • Peng Sun
  • Jiawei Zhang
  • Melvyn Sim
    • Categories Robust Optimization, Second-Order Cone Programming, Stochastic Programming Tags , , ,

    Stochastic programming, despite its immense modeling capabilities, is well known to be computationally excruciating. In this paper, we introduce a unified framework of approximating multiperiod stochastic programming from the perspective of robust optimization. Specifically, we propose a framework that integrates multistage modeling with safeguarding constraints. The framework is computationally tractable in the form of second … Read more

    A Robust Optimization Framework for Analyzing Distribution Systems with Transshipment

  • Mabel C. Chou
  • Melvyn Sim
  • Rick So
    • Categories Robust Optimization, Stochastic Programming, Supply Chain Management Tags , , ,

    This paper studies a distribution system consisting of multiple retail locations with transshipment operations among the retailers. Due to the difficulty in computing the optimal solution imposed by the transshipment operations and in estimating shortage cost from a practical perspective, we propose a robust optimization framework for analyzing the impact of transshipment operations on such … Read more

    Uniform Laws of Large Numbers for Set-Valued Mappings and Subdifferentials of Random Functions

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

    We derive a uniform (strong) Law of Large Numbers (LLN) for random set-valued mappings. The result can be viewed as an extension of both, a uniform LLN for random functions and LLN for random sets. We apply the established results to a consistency analysis of stationary points of sample average approximations of nonsmooth stochastic programs. … Read more

    On the Implementation of Interior Point Decomposition Algorithms for Two-Stage Stochastic Conic

  • Sanjay Mehrotra
  • M. Gokhan Ozevin
    • Categories Finance and Economics, Linear, Cone and Semidefinite Programming, Stochastic Programming Tags , , , , ,

    In this paper we develop a practical primal interior decomposition algorithm for two-stage stochastic programming problems. The framework of this algorithm is similar to the framework in Mehrotra and \”{Ozevin} \cite{MO04a,MO04b} and Zhao \cite{GZ01}, however their algorithm is altered in a simple yet fundamental way to achieve practical performance. In particular, this new algorithm weighs … Read more

    A Robust Optimization Perspective of Stochastic Programming

  • Xin Chen
  • Peng Sun
  • Melvyn Sim
    • Categories Robust Optimization, Stochastic Programming Tags , ,

    In this paper, we introduce an approach for constructing uncertainty sets for robust optimization using new deviation measures for bounded random variables known as the forward and backward deviations. These deviation measures capture distributional asymmetry and lead to better approximations of chance constraints. We also propose a tractable robust optimization approach for obtaining robust solutions … Read more

    Non-Linear Stochastic Fractional Programming Models of Financial Derivatives

  • Vincent Charles
  • D Dutta
    • Categories Finance and Economics, Stochastic Programming Tags , ,

    Non-Linear Stochastic Fractional programming models provide numerous insights into a wide variety of areas such as in financial derivatives. Portfolio optimization has been one of the important research fields in modern finance. The most important character within this optimization problem is the uncertainty of the future returns on assets. The objective of this study is … Read more

    Linear Stochastic Fractional Programming with Sum-of-Probabilistic-Fractional Objective

  • Vincent Charles
  • D Dutta
    • Categories Stochastic Programming Tags , , ,

    Fractional programming deals with the optimization of one or several ratios of functions subject to constraints. Most of these optimization problems are not convex while some of them are still generalised convex. After about forty years of research, well over one thousand articles have appeared on applications, theory and solution methods for various types of … Read more

    Stochastic Mathematical Programs with Equilibrium Constraints, Modeling and Sample Average Approximation

  • Alexander Shapiro
  • Huifu Xu
    • Categories Complementarity and Variational Inequalities, Stochastic Programming Tags , , , , , ,

    In this paper, we discuss the sample average approximation (SAA) method applied to a class of stochastic mathematical programs with variational (equilibrium) constraints. To this end, we briefly investigate piecewise structure and directional differentiability of both — the lower level equilibrium solution and objective integrant. We show almost sure convergence of optimal values, optimal solutions … Read more

    On Complexity of Multistage Stochastic Programs

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

    In this paper we derive estimates of the sample sizes required to solve a multistage stochastic programming problem with a given accuracy by the (conditional sampling) sample average approximation method. The presented analysis is self contained and is based on a, relatively elementary, one dimensional Cramer’s Large Deviations Theorem. Citation Working paper, Georgia Institute of … Read more

    Two-Stage Stochastic Semidefinite Programming and Decomposition Based Interior Point Methods

  • Sanjay Mehrotra
  • M. Gokhan Ozevin
    • Categories Semi-definite Programming, Stochastic Programming Tags , , ,

    We introduce two-stage stochastic semidefinite programs with recourse and present a Benders decomposition based linearly convergent interior point algorithms to solve them. This extends the results of Zhao, who showed that the logarithmic barrier associated with the recourse function of two-stage stochastic linear programs with recourse behaves as a strongly self-concordant barrier on the first … Read more