An global Jacobian smoothing algorithm for nonlinear complementarity problems

Abstract

In this paper, we use the smoothing Jacobian strategy to propose a new algorithm for solving complementarity problems based on its reformulation as a nonsmooth system of equations. This algorithm can be seen as a generalization of the one proposed in [18]. We develop its global convergence theory and under certain assumptions, we demonstrate that the proposed algorithm converges locally and, q-superlinearly or q-quadratically to a solution of the problem. Some numerical experiments show a good performance of this algorithm.

Keywords

• Nonlinear complementarity problems
• complementarity function
• generalized Newton methods
• Jacobian smoothing method
• global convergence
• superlinear convergence