A regularization SAA scheme for a stochastic mathematical program with complementarity constraints
type: Item
instance of: scholarly article
title: A regularization SAA scheme for a stochastic mathematical program with complementarity constraints
zbMATH Open document ID: 1406.90086
DOI: 10.1155/2014/321010
author: Yu-Xin Li
author: Jie Zhang
author: Zun-Quan Xia
published in: Journal of Applied Mathematics
publication date: 2019-02-01T00:00:00Z
review text: Summary: To reflect uncertain data in practical problems, stochastic versions of the mathematical program with complementarity constraints (MPCC) have drawn much attention in the recent literature. Our concern is the detailed analysis of convergence properties of a regularization sample average approximation (SAA) method for solving a stochastic mathematical program with complementarity constraints (SMPCC). The analysis of this regularization method is carried out in three steps: First, the almost sure convergence of optimal solutions of the regularized SAA problem to that of the true problem is established by the notion of epiconvergence in variational analysis. Second, under MPCC-MFCQ, which is weaker than MPCC-LICQ, we show that any accumulation point of Karash-Kuhn-Tucker points of the regularized SAA problem is almost surely a kind of stationary point of SMPCC as the sample size tends to infinity. Finally, some numerical results are reported to show the efficiency of the method proposed.
Mathematics Subject Classification ID: 90C15
Mathematics Subject Classification ID: 90C33
zbMATH DE Number: 7010597
Wikidata QID: Q59050891
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/321010
OpenAlex ID: W2031519247
DBLP publication ID: journals/jam/LiZX14
description: scientific article; zbMATH DE number 7010597