文献类型：期刊文献

英文题名：Optimality Analysis of a Class of Semi-infinite Programming Problems

作者：Feng, Zhi Guo[1];Chen, Fei[2];Chen, Lin[2,3];Yiu, Ka Fai Cedric[4]

机构：[1]Guangdong Ocean Univ, Fac Math & Comp Sci, Zhanjiang, Guangdong, Peoples R China;[2]Chongqing Normal Univ, Sch Math Sci, Chongqing, Peoples R China;[3]Univ Elect Sci & Technol China, Sch Math Sci, Chengdu, Sichuan, Peoples R China;[4]Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

年份：2020

卷号：186

期号：2

起止页码：398

外文期刊名：JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS

收录：SCI-EXPANDED(收录号：WOS:000545885500002)、、Scopus(收录号：2-s2.0-85087559628)、WOS

基金：This paper is supported by the grant of National Natural Science Foundation of China (Nos. 11771064, 11991020, 11991023), the Natural Science Foundation of Chongqing (cstc2019jcyj-zdxmX0016), the grant of Guangdong Basic and Applied Basic Research Foundation (No. 2020A1515010463), the program for scientific research start-up funds of Guangdong Ocean University, the grant of Chongqing Normal University (No. 17XLB010). The fourth author is supported by RGC Grant PolyU. (152245/18E) and PolyU Grant ZZGS.

语种：英文

外文关键词：Semi-infinite programming; Fixed-point theorem; Filter design; Beamformer design

外文摘要：In this paper, we consider a class of semi-infinite programming problems with a parameter. As the parameter increases, we prove that the optimal values decrease monotonically. Moreover, the limit of the sequence of optimal values exists as the parameter tends to infinity. In finding the limit, we decompose the original optimization problem into a series of subproblems. By calculating the maximum optimal values to the subproblems and applying a fixed-point theorem, we prove that the obtained maximum value is exactly the limit of the sequence of optimal values under certain conditions. As a result, the limit can be obtained efficiently by solving a series of simplified subproblems. Numerical examples are provided to verify the limit obtained by the proposed method.