文献类型：期刊文献

英文题名：Asymptotic analysis for a stochastic semidefinite programming

作者：Zhang, Jie[1];Lin, Shuang[1];Zhang, Yi[2]

机构：[1]Liaoning Normal Univ, Sch Math, Dalian 116029, Peoples R China;[2]East China Univ Sci & Technol, Dept Math, Sch Sci, Shanghai 200237, Peoples R China

年份：2021

卷号：49

期号：2

起止页码：164

外文期刊名：OPERATIONS RESEARCH LETTERS

收录：;EI(收录号：20210109725056);WOS:【SCI-EXPANDED(收录号:WOS:000624944700003)】；

基金：We would like to thank the Area Editor and anonymous referees for valuable comments which help us significantly consolidate the paper. The research is supported by the National Natural Science Foundation of China under project Grant No. 11671183, Natural Science Foundation of Liaoning Province, China under project Grant No. 2019MS217, Liaoning BaiQianWan Talents Program, China and Young Top Talents Project of "Xingliao Talents Program", China.

语种：英文

外文关键词：Stochastic semidefinite programming; Asymptotic analysis; Sample average approximation (SAA); Convergence in distribution

摘要：Stochastic semidefinite programming (SSDP) is a new class of optimization problems with a wide variety of applications. In this article, asymptotic analysis results of sample average approximation estimator for SSDP are established. Asymptotic analysis result already existing for stochastic nonlinear programming is extended to SSDP, that is, the conditions ensuring the convergence in distribution of sample average approximation estimator for SSDP to a multivariate normal are obtained and the corresponding covariance matrix is described in a closed form. (C) 2020 Elsevier B.V. All rights reserved.