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

作者：Dong, Li; Tang, Jingyong; Song, Xinyu^*

来源：International Journal of Computer Mathematics, 2018, 95(4): 739-751.

DOI：10.1080/00207160.2017.1296140

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

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.

• 出版日期2018
• 单位信阳师范学院