A Nonlinear Lagrange Algorithm for Minimax Problems with General Constraints. (2nd June 2016)

• Record Type: Journal Article
• Authors: He, Suxiang; Liu, Xiangfeng; Wang, Chuanmei
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 6(2016)
• Page Start: 680
• Page End: 698
• Publication Date: 2016-06-02
• Subjects: Minimax problems with general constraints -- nonlinear Lagrange algorithm -- penalty parameter -- rate of convergence; 90C47 -- 90C30 -- 65K05 -- 49K35; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1155157
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: This article presents a novel nonlinear Lagrange algorithm for solving minimax optimization problems with both inequality and equality constraints, which eliminates the nonsmoothness of the considered problems and the numerical difficulty of the penalty method. The convergence of the proposed algorithm is analyzed under some mild assumptions, in which the sequence of the generated solutions converges locally to a Karush-Kuhn-Tucker solution at a linear rate when the penalty parameter is less than a threshold and the error bound of the solutions is also obtained. Finally, the detailed numerical results for several typical testproblems are given in order to show the performance of the proposed algorithm.