Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/91238
Title: Convergence analysis of sample average approximation of two-stage stochastic generalized equations
Authors: Chen, XJ 
Shapiro, A
Sun, HL
Issue Date: 2019
Source: SIAM journal on optimization, 2019, v. 29, no. 1, p. 135-161
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 noncooperative games of two players.
Keywords: Two-stage stochastic generalized equations
Sample average approximation
Convergence
Exponential rate
Monotone multifunctions
Publisher: Society for Industrial and Applied Mathematics
Journal: SIAM journal on optimization 
ISSN: 1052-6234
EISSN: 1095-7189
DOI: 10.1137/17M1162822
Rights: © 2019 Society for Industrial and Applied Mathematics
Posted with permission of the publisher.
The following publication Chen, X., Shapiro, A., & Sun, H. (2019). Convergence analysis of sample average approximation of two-stage stochastic generalized equations. SIAM Journal on Optimization, 29(1), 135-161 is available at https://dx.doi.org/10.1137/17M1162822
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