A smooth Newton method with 3-1 piecewise NCP function for generalized nonlinear complementarity problem

ABSTRACT

In this paper, based on the 3-1 piecewise nonlinear complementarity problem (NCP) function, we proposed a smoothing Newton-type method for the generalized nonlinear complementarity problem (GNCP) with a modified non-monotone line search. The algorithm for a GNCP is more difficult than that for an NCP, because two functions must be considered in the problem. We reformulate the (GNCP) to a smoothing system of equations by two independent variables, and then develop a smoothing Newton-type method for solving it. Under reasonable conditions, we obtain the global convergent properties. Also, the numerical experiments are reported in this paper.

KEYWORDS:

• Generalized nonlinear complementarity problem
• piecewise NCP function
• non-monotone
• global convergence

2000 AMS CLASSIFICATIONS:

• 90C30
• 65K05

Acknowledgements

The authors are thankful to the anonymous referees for their valuable suggestions and comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Additional, this work is supported by the National Natural Science Foundation of China [No. 11101115, 61572011], the Natural Science Foundation of Hebei Province [No. A2014201033], the Key Research Foundation of Education Bureau of Hebei Province [No. ZD2015069].