A modified damped Gauss–Newton method for non-monotone weighted linear complementarity problems. (4th May 2022)

• Record Type: Journal Article
• Authors: Tang, Jingyong; Zhou, Jinchuan
• Is Part Of: Optimization methods and software. Volume 37:Number 3(2022)
• Page Start: 1145
• Page End: 1164
• Publication Date: 2022-05-04
• Subjects: Weighted linear complementarity problem -- damped Gauss–Newton method -- local error bound -- quadratic convergence; 90C33 -- 90C56; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2021.1903007
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : We consider the weighted linear complementarity problem (denoted by wLCP). Many numerical algorithms have been proposed for solving the monotone wLCP. In this paper, we propose a damped Gauss–Newton method to solve the non-monotone wLCP which is designed based on a derivative-free non-monotone line search. We show that the proposed method is well defined and it is globally convergent without any problem assumptions. Moreover, we analyze the local quadratic convergence of the proposed method under the non-singularity condition and the local error bound condition, respectively. Our method not only has encouraging local convergence properties but also can be used to solve non-monotone wLCPs. Preliminary numerical results are reported.