文献类型：期刊文献

英文题名：LIMIT ANALYSIS FOR THE OPTIMAL VALUE OF A CLASS OF MINIMAX OPTIMIZATION PROBLEMS

作者：Chen, Fei[1];Feng, Zhi Guo[2];Yiu, K. F. C.[3]

机构：[1]Chongqing Normal Univ, Sch Math Sci, Chongqing, Peoples R China;[2]Guangdong Ocean Univ, Fac Math & Comp Sci, Zhanjiang, Peoples R China;[3]Hongkong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China

年份：2020

卷号：16

期号：2

起止页码：315

外文期刊名：PACIFIC JOURNAL OF OPTIMIZATION

收录：SCI-EXPANDED(收录号：WOS:000708316800008)、、WOS

基金：This paper is supported by the grant of National Science Foundation of Guangdong Province (No. 2020A1515010463), the grant of Chongqing Science and Technology Commission (No. cstc2017jcyjAX0161), the grant of Chongqing Normal University (No. 17XLB010), and program for scientific research start-up funds of Guangdong Ocean University. The third author is supported by RGC Grant PolyU. 152200/14E and PolyU Grant ZZGS.

语种：英文

外文关键词：minimax optimization; semi-infinite programming; fixed point theorem

外文摘要：A novel method is presented to analyze the limit for the optimal value of a class of minimax optimization problems with parameter. The minimax optimization problems can be transformed into semi-infinite programming (SIP) problems, and the optimal value series of the SIP problems with parameter are analyzed. First, we obtain that the optimal values of the cost function is monotonically decreasing as the parameter increases, and then the limit exists and can be computed by choosing a sufficiently large parameter. Next, we propose a novel method to obtain the limit of the optimal values by introducing a series of simplified subproblems. We derive the conditions and apply the fixed point theorem to prove that the function obtained by the proposed method is exactly the continuous limit function when the parameter tends to infinity, and the maximum value obtained by the proposed method is exactly the limit of optimal value series as the parameter tends to infinity. For illustration, numerical experiments are demonstrated to show the effectiveness and efficiency of the proposed method.