A non-monotone inexact regularized smoothing Newton method for solving nonlinear complementarity problems

Abstract

In the paper [S.P. Rui and C.X. Xu, A smoothing inexact Newton method for nonlinear complementarity problems, J. Comput. Appl. Math. 233 (2010), pp. 2332–2338], the authors proposed an inexact smoothing Newton method for nonlinear complementarity problems (NCP) with the assumption that F is a uniform P function. In this paper, we present a non-monotone inexact regularized smoothing Newton method for solving the NCP which is based on Fischer–Burmeister smoothing function. We show that the proposed algorithm is globally convergent and has a locally superlinear convergence rate under the weaker condition that F is a P ₀ function and the solution of NCP is non-empty and bounded. Numerical results are also reported for the test problems, which show the effectiveness of the proposed algorithm.

Keywords:

• nonlinear complementarity problem
• non-monotone inexact smoothing Newton method
• global convergence
• local superlinear convergence

2000 AMS Subject Classifications :

• 90C33
• 65K05

Acknowledgements

This work is supported by National Natural Science Foundations of China 61072144.