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论文类型：期刊论文
发表时间：2012-04-01
发表刊物：PACIFIC JOURNAL OF OPTIMIZATION
收录刊物：SCIE、Scopus
卷号：8
期号：2
页面范围：361-386
ISSN号：1348-9151
关键字：stochastic generalized Nash equilibrium problem; sample average approximation method; exponential rate; Clarke's generalized Jacobian; smoothing Newton method
摘要：In this paper, a type of one stage stochastic generalized Nash equilibrium problem (SGNEP) is solved by the sample average approximation (SAA) method. It is demonstrated that the sequence of Karush-Kuhn-Tucker points of SAA problems converges to a Karush-Kuhn-Tucker point of the true problem with probability one at an exponential rate as the sample size tends to infinity. To implement the SAA method in practice, the smoothing Newton method is introduced. In the case when the expectation constraint functions in the true problem are strongly additive, the nonsingularity of Clarke's generalized Jacobian of the SAA Karush-Kuhn-Tucker system, which is required in the convergence analysis of smoothing Newton method, is demonstrated under the so-called SGNEP-LICQ and SGNEP-SOSC. For this special case, preliminary numerical results are reported to show the efficiency of the method.