A Modified Nonsmooth Levenberg–Marquardt Algorithm for the General Mixed Complementarity Problem

As is well known, the mixed complementarity problem is equivalent to a nonsmooth equation by using a median function. By investigating the generalized Jacobi of a composite vector-valued maximum function, a nonsmooth Levenberg–Marquardt algorithm is proposed in this paper. In the present algorithm,...

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Autores principales:	Linsen Song, Yan Gao
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/20c462cdfe074fccacaca52159a3cdb8
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spelling	oai:doaj.org-article:20c462cdfe074fccacaca52159a3cdb82021-11-29T00:56:05ZA Modified Nonsmooth Levenberg–Marquardt Algorithm for the General Mixed Complementarity Problem1563-514710.1155/2021/7249349https://doaj.org/article/20c462cdfe074fccacaca52159a3cdb82021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/7249349https://doaj.org/toc/1563-5147As is well known, the mixed complementarity problem is equivalent to a nonsmooth equation by using a median function. By investigating the generalized Jacobi of a composite vector-valued maximum function, a nonsmooth Levenberg–Marquardt algorithm is proposed in this paper. In the present algorithm, we adopt a new LM parameter form and discuss the local convergence rate under the local error bound condition, which is weaker than nonsingularity. Finally, the numerical experiments and the application for the real-time pricing in smart grid illustrate the effectiveness of the algorithm.Linsen SongYan GaoHindawi LimitedarticleEngineering (General). Civil engineering (General)TA1-2040MathematicsQA1-939ENMathematical Problems in Engineering, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
spellingShingle	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939 Linsen Song Yan Gao A Modified Nonsmooth Levenberg–Marquardt Algorithm for the General Mixed Complementarity Problem
description	As is well known, the mixed complementarity problem is equivalent to a nonsmooth equation by using a median function. By investigating the generalized Jacobi of a composite vector-valued maximum function, a nonsmooth Levenberg–Marquardt algorithm is proposed in this paper. In the present algorithm, we adopt a new LM parameter form and discuss the local convergence rate under the local error bound condition, which is weaker than nonsingularity. Finally, the numerical experiments and the application for the real-time pricing in smart grid illustrate the effectiveness of the algorithm.
format	article
author	Linsen Song Yan Gao
author_facet	Linsen Song Yan Gao
author_sort	Linsen Song
title	A Modified Nonsmooth Levenberg–Marquardt Algorithm for the General Mixed Complementarity Problem
title_short	A Modified Nonsmooth Levenberg–Marquardt Algorithm for the General Mixed Complementarity Problem
title_full	A Modified Nonsmooth Levenberg–Marquardt Algorithm for the General Mixed Complementarity Problem
title_fullStr	A Modified Nonsmooth Levenberg–Marquardt Algorithm for the General Mixed Complementarity Problem
title_full_unstemmed	A Modified Nonsmooth Levenberg–Marquardt Algorithm for the General Mixed Complementarity Problem
title_sort	modified nonsmooth levenberg–marquardt algorithm for the general mixed complementarity problem
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/20c462cdfe074fccacaca52159a3cdb8
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A Modified Nonsmooth Levenberg–Marquardt Algorithm for the General Mixed Complementarity Problem

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