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Convergence Analysis of Sample Average Approximation of Two-stage Stochastic Generalized Equations

Xiaojun Chen (xiaojun.chen***at***polyu.edu.hk)
Alexander Shapiro (alex.shapiro***at***isye.gatech.edu)
Hailin Sun (hlsun***at***njust.edu.cn)

Abstract: A solution of two-stage stochastic generalized equations is a pair: a first stage solution which is independent of realization of the random data and a second stage solution which is a function of random variables. This paper studies convergence of the sample average approximation of two-stage stochastic nonlinear generalized equations. In particular an exponential rate of the convergence is shown by using the perturbed partial linearization of functions. Moreover, sufficient conditions for the existence, uniqueness, continuity and regularity of solutions of two-stage stochastic generalized equations are presented under an assumption of monotonicity of the involved functions. These theoretical results are given without assuming relatively complete recourse, and are illustrated by two-stage stochastic non-cooperative games of two players.

Keywords: Two-stage stochastic generalized equations, sample average approximation, convergence, exponential rate, monotone multifunctions

Category 1: Stochastic Programming

Citation: X. Chen, A. Shapiro and H. Sun, Convergence analysis of sample average approximation of two-stage stochastic generalized equations, submitted, 2018.

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Entry Submitted: 01/11/2018
Entry Accepted: 01/11/2018
Entry Last Modified: 01/11/2018

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