Least Change Secant Update Methods for Nonlinear Complementarity Problem

Abstract

In this work, we introduce a family of Least Change Secant Update Methods for solving Nonlinear Complementarity Problems based on its reformulation as a nonsmooth system using the one-parametric class of nonlinear complementarity functions introduced by Kanzow and Kleinmichel. We prove local and superlinear convergence for the algorithms. Some numerical experiments show a good performance of this algorithm. MSC: 90C30, 90C33, 90C53

Keywords

• Nonsmooth systems
• Nonlinear Complementarity Problems
• generalized Jacobians
• Quasi-Newton methods
• Least Change Secant Update Methods
• local convergence