Optimality Analysis of a Class of Semi-infinite Programming Problems

Zhi Guo Feng, Fei Chen, Lin Chen, Ka Fai Cedric Yiu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)398-411
Number of pages14
JournalJournal of Optimization Theory and Applications
Volume186
Issue number2
DOIs
Publication statusPublished - Aug 2020

Keywords

  • Beamformer design
  • Filter design
  • Fixed-point theorem
  • Semi-infinite programming

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

Cite this