A Nonsmooth L-M Method for Solving the Generalized Nonlinear Complementarity Problem over a Polyhedral Cone

A Nonsmooth L-M Method for Solving the Generalized Nonlinear Complementarity Problem over a... In this paper the generalized nonlinear complementarity problem (GNCP) defined on a polyhedral cone is reformulated as a system of nonsmooth equations. Based on this reformulation, the famous Levenberg-Marquardt (L-M) algorithm is employed to obtain its solution. Theoretical results that relate the stationary points of the merit function to the solution of the GNCP are presented. Under mild assumptions, we show that the L-M algorithm is both globally and superlinearly convergent. Moreover, a method to calculate a generalized Jacobian is given and numerical experimental results are presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

A Nonsmooth L-M Method for Solving the Generalized Nonlinear Complementarity Problem over a Polyhedral Cone

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Publisher
Springer-Verlag
Copyright
Copyright © 2005 by Springer
Subject
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-005-0823-4
Publisher site
See Article on Publisher Site

Abstract

In this paper the generalized nonlinear complementarity problem (GNCP) defined on a polyhedral cone is reformulated as a system of nonsmooth equations. Based on this reformulation, the famous Levenberg-Marquardt (L-M) algorithm is employed to obtain its solution. Theoretical results that relate the stationary points of the merit function to the solution of the GNCP are presented. Under mild assumptions, we show that the L-M algorithm is both globally and superlinearly convergent. Moreover, a method to calculate a generalized Jacobian is given and numerical experimental results are presented.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Jun 1, 2005

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