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论文类型：期刊论文

发表时间：2015-05-15

发表刊物：JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

收录刊物：SCIE、EI、Scopus

文献类型：J

卷号：280

期号：1

页面范围：202-216

ISSN号：0377-0427

关键字：Sample average approximation; Log-exponential function; Stochastic mathematical program with general vertical complementarity constraints; Stochastic Stackelberg game

摘要：Based on the log-exponential function, a sample average approximation (SAA) regularization method is proposed for solving a stochastic mathematical program with general vertical complementarity constraints (SMPVCC) considered by Birbil et al. (2006). Detailed convergence analysis of this method is investigated. It is demonstrated that under some regularity conditions, any accumulation point of the sequence of optimal solutions of SAA regularized problem is almost surely an optimal solution of the SMPVCC as the parameter tends to zero and the sample size tends to infinity. Furthermore, the optimal value sequence of SPA regularized problem converges to the optimal value of SMPVCC with exponential convergence rate with probability one and a sequence of stationary points of regularized SAA problem converges almost surely to a stationary point of SMPVCC. Finally, we show that a stochastic Stackelberg game can be formulated as a SMPVCC problem and an equilibrium solution can be obtained by the method proposed. (C) 2014 Elsevier B.V. All rights reserved.