A new semismooth Newton method for NCPs based on the penalized KK function

Abstract

In this paper, based on the Kanzow-Kleinmichel (KK) function, we introduce a new nonlinear complementarity problem (NCP) function: penalized KK function. We show that the function possesses desirable properties similar to those of the KK function. Based on this new NCP function, we reformulate the NCP to a system of semismooth equations. We also propose a new semismooth Levenberg–Marquardt method to solve the system of semismooth equations that employs both trust region techniques and line searches. The global and quadratic convergence properties can be established under very mild assumptions. Numerical results show the effectiveness of the proposed algorithm and also indicate that superior behaviour of the proposed new NCP function.

Keywords:

• nonlinear complementarity problem
• semismooth Levenberg–Marquardt method
• generalized Jacobians
• global convergence
• quadratic convergence

2000 AMS Subject Classifications :

• 90C33
• 65K05

Acknowledgement

This work was supported by the National Natural Science Foundation of China (61101208,61072144).