A modified damped Gauss–Newton method for non-monotone weighted linear complementarity problems

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.

Keywords:

• Weighted linear complementarity problem
• damped Gauss–Newton method
• local error bound
• quadratic convergence

2010 Mathematics Subject Classifications:

• 90C33
• 90C56

Acknowledgments

Research of this paper was partly supported by National Natural Science Foundation of China (11771255), Young Innovation Teams of Shandong Province (2019KJI013), Program of Science and Technology Activities for Overseas Students in Henan Province in 2020 and Nanhu Scholars Program for Young Scholars of Xinyang Normal University. We are very grateful to the three referees for their valuable comments on the paper, which have considerably improved the paper

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China [Grant Number 11771255].

Notes on contributors

Jingyong Tang

Jingyong Tang received the Master's degree in Operations Research from Qufu Normal University, Rizhao, P.R. China in 2006 and the PhD degree in Applied Mathematics from Shanghai Jiaotong University, Shanghai, P.R. China in 2012. His research interests are numerical algorithms for cone optimization problems and complementarity problems.

Jinchuan Zhou

Jinchuan Zhou received the Master's degree in Operations Research from Qufu Normal University, Rizhao, P.R. China in 2006 and the PhD degree in Operations Research from Beijing Jiaotong University, Beijing, P.R. China in 2009. His research interests include cone programming, variational analysis and complementarity problems.