Open AccessA smooth Levenberg-Marquardt method without nonsingularity condition for wLCP
Author(s) -
Xiaorui He,
Jingyong Tang
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022497
Subject(s) - levenberg–marquardt algorithm , line search , mathematics , monotone polygon , rate of convergence , complementarity (molecular biology) , quadratic equation , trust region , convergence (economics) , nonlinear system , nonlinear complementarity problem , quadratic function , mathematical optimization , algorithm , complementarity theory , computer science , artificial neural network , geometry , artificial intelligence , computer network , channel (broadcasting) , physics , computer security , quantum mechanics , biology , economics , radius , genetics , economic growth
In this paper we consider the weighted Linear Complementarity Problem (wLCP). By using a smooth weighted complementarity function, we reformulate the wLCP as a smooth nonlinear equation and propose a Levenberg-Marquardt method to solve it. The proposed method differentiates itself from the current Levenberg-Marquardt type methods by adopting a simple derivative-free line search technique. It is shown that the proposed method is well-defined and it is globally convergent without requiring wLCP to be monotone. Moreover, the method has local sub-quadratic convergence rate under the local error bound condition which is weaker than the nonsingularity condition. Some numerical results are reported.