Convergence properties of a class of exact penalty methods for semi-infinite optimization problems

作     者：Ju, Jiachen Liu, Qian 

作者机构：Shandong Normal Univ Sch Math & Stat Jinan Shandong Peoples R China 

出 版 物：《MATHEMATICAL METHODS OF OPERATIONS RESEARCH》 (运筹学研究中的数学方法)

年 卷 期：2020年第91卷第3期

页      面：383-403页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：National Natural Science Foundation of China [11271233  11271226] 

主　　题：Exact penalty function Semi-infinite programming Convergence Nonlinear programming 

摘      要：In this paper, a new class of unified penalty functions are derived for the semi-infinite optimization problems, which include many penalty functions as special cases. They are proved to be exact in the sense that under Mangasarian-Fromovitz constraint qualification conditions, a local solution of penalty problem is a corresponding local solution of original problem when the penalty parameter is sufficiently large. Furthermore, global convergence properties are shown under some conditions. The paper is concluded with some numerical examples proving the applicability of our methods to PID controller design and linear-phase FIR digital filter design.