Least Change Secant Update Methods for Nonlinear Complementarity Problem

Main Article Content

Favián Arenas A https://orcid.org/0000-0002-7781-7559
H J Martínez http://orcid.org/0000-0001-9747-0671
Rosana Pérez https://orcid.org/0000-0003-0279-8522

Keywords

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

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

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