A non-monotone inexact non-interior continuation method based on a parametric smoothing function for LWCP

Abstract

This paper considers the linear weighted complementarity problem (denoted by LWCP). We introduce a parametric smoothing function which is a broad class of smoothing functions for the LWCP and enjoys some favourable properties. Based on this function, we propose a new non-interior continuation method for solving the LWCP. In general, the non-interior continuation method consists of finding an exact solution of a system of equations at each iteration, which may be cumbersome if one is solving a large-scale problem. To overcome this difficulty, our method uses an inexact Newton method to solve the corresponding linear system approximately and adopts a non-monotone line search to obtain a step size. Under suitable assumptions, we show that the proposed method is globally and locally quadratically convergent. Preliminary numerical results are also reported.

Keywords:

• Linear weighted complementarity problem
• non-interior continuation method
• inexact Newton method
• non-monotone line search
• quadratical convergence

2010 AMS SUBJECT CLASSIFICATIONS:

• 90C33
• 65K05

Acknowledgements

The authors are grateful to the referees for their careful reading and helpful suggestions that improved the paper greatly.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Research of this paper was partly supported by National Natural Science Foundation of China [11371306, 11671346], Basic and Frontier Technology Research Project of Henan Province [162300410071] and Nanhu Scholars Program for Young Scholars of XYNU and Nanhu Scholars Program of XYNU.