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论文类型：期刊论文
发表时间：2012-10-01
发表刊物：APPLICATIONS OF MATHEMATICS
收录刊物：SCIE、EI、Scopus
卷号：57
期号：5
页面范围：477-502
ISSN号：0862-7940
关键字：smoothing SAA method; log-exponential function; stochastic mathematical program with complementarity constraints; almost sure convergence
摘要：A smoothing sample average approximation (SAA) method based on the log-exponential function is proposed for solving a stochastic mathematical program with complementarity constraints (SMPCC) considered by Birbil et al. (S. I. Birbil, G. Gurkan, O. Listes: Solving stochastic mathematical programs with complementarity constraints using simulation, Math. Oper. Res. 31 (2006), 739-760). It is demonstrated that, under suitable conditions, the optimal solution of the smoothed SAA problem converges almost surely to that of the true problem as the sample size tends to infinity. Moreover, under a strong second-order sufficient condition for SMPCC, the almost sure convergence of Karash-Kuhn-Tucker points of the smoothed SAA problem is established by Robinson's stability theory. Some preliminary numerical results are reported to show the efficiency of our method.