An almost smooth equation reformulation to the nonlinear complementarity problem and Newton's method

Abstract

In this paper, we propose a semismooth equation reformulation to the nonlinear complementarity problem. The reformulation function enjoys a nice property that it is continuously differentiable everywhere except at the solution, which enables us to use a smooth version of Newton's method to solve. It is semismooth (almost smooth) at any solution of the problem. In particular, if the solution set of the problem is a singleton, then the reformulation function is a basic strongly almost smooth function. We propose a Newton method to solve the equations and establish its global and superlinear convergence. The limited numerical results show that the method works well.

Keywords:

• nonlinear complementarity problem
• almost smooth equation
• Newton's method

Acknowledgements

This work was supported by the NSF of China Grant 10771057 and 10771057.