A class of smoothing SAA methods for a stochastic mathematical program with complementarity constraints

Indexed by:期刊论文

Journal:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Included Journals:SCIE

Volume:387

Issue:1

Page Number:201-220

ISSN No.:0022-247X

Key Words:Sample average approximation; Smoothing method; Stochastic mathematical program with complementarity constraints; Almost sure convergence

Abstract:A class of smoothing sample average approximation (SAA) methods is proposed for solving the stochastic mathematical program with complementarity constraints (SMPCC) considered by Birbil et al. [S.I. Birbil, G. Gfirkan, O. Listes, Solving stochastic mathematical programs with complementarity constraints using simulation, Math. Oper. Res. 31 (2006) 739-760]. The almost sure convergence of optimal solutions of the smoothed SAA problem to that of the true problem is established by the notion of epi-convergence in variational analysis. It is demonstrated that, under suitable conditions, any accumulation point of Karash-Kuhn-Tucker points of the smoothed SAA problem is almost surely a kind of stationary point of SMPCC as the sample size tends to infinity. Moreover, under a strong second-order sufficient condition for SMPCC, the exponential convergence rite of the sequence of Karash-Kuhn-Tucker points of the smoothed SAA problem is investigated through an application of Robinson's stability theory. Some preliminary numerical results are reported to show the efficiency of proposed method. Crown Copyright (C) 2011 Published by Elsevier Inc. All rights reserved.

Date of Publication:2012-03-01