Cargando…
A non-monotone pattern search approach for systems of nonlinear equations
In this paper, a new pattern search is proposed to solve the systems of nonlinear equations. We introduce a new non-monotone strategy which includes a convex combination of the maximum function of some preceding successful iterates and the current function. First, we produce a stronger non-monotone...
Autores principales: | , , |
---|---|
Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Taylor & Francis
2017
|
Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6235546/ https://www.ncbi.nlm.nih.gov/pubmed/30487705 http://dx.doi.org/10.1080/00207160.2017.1413552 |
_version_ | 1783370890007805952 |
---|---|
author | Amini, Keyvan Kimiaei, Morteza Khotanlou, Hassan |
author_facet | Amini, Keyvan Kimiaei, Morteza Khotanlou, Hassan |
author_sort | Amini, Keyvan |
collection | PubMed |
description | In this paper, a new pattern search is proposed to solve the systems of nonlinear equations. We introduce a new non-monotone strategy which includes a convex combination of the maximum function of some preceding successful iterates and the current function. First, we produce a stronger non-monotone strategy in relation to the generated strategy by Gasparo et al. [Nonmonotone algorithms for pattern search methods, Numer. Algorithms 28 (2001), pp. 171–186] whenever iterates are far away from the optimizer. Second, when iterates are near the optimizer, we produce a weaker non-monotone strategy with respect to the generated strategy by Ahookhosh and Amini [An efficient nonmonotone trust-region method for unconstrained optimization, Numer. Algorithms 59 (2012), pp. 523–540]. Third, whenever iterates are neither near the optimizer nor far away from it, we produce a medium non-monotone strategy which will be laid between the generated strategy by Gasparo et al. [Nonmonotone algorithms for pattern search methods, Numer. Algorithms 28 (2001), pp. 171–186] and Ahookhosh and Amini [An efficient nonmonotone trust-region method for unconstrained optimization, Numer. Algorithms 59 (2012), pp. 523–540]. Reported are numerical results of the proposed algorithm for which the global convergence is established. |
format | Online Article Text |
id | pubmed-6235546 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2017 |
publisher | Taylor & Francis |
record_format | MEDLINE/PubMed |
spelling | pubmed-62355462018-11-26 A non-monotone pattern search approach for systems of nonlinear equations Amini, Keyvan Kimiaei, Morteza Khotanlou, Hassan Int J Comput Math Original Article In this paper, a new pattern search is proposed to solve the systems of nonlinear equations. We introduce a new non-monotone strategy which includes a convex combination of the maximum function of some preceding successful iterates and the current function. First, we produce a stronger non-monotone strategy in relation to the generated strategy by Gasparo et al. [Nonmonotone algorithms for pattern search methods, Numer. Algorithms 28 (2001), pp. 171–186] whenever iterates are far away from the optimizer. Second, when iterates are near the optimizer, we produce a weaker non-monotone strategy with respect to the generated strategy by Ahookhosh and Amini [An efficient nonmonotone trust-region method for unconstrained optimization, Numer. Algorithms 59 (2012), pp. 523–540]. Third, whenever iterates are neither near the optimizer nor far away from it, we produce a medium non-monotone strategy which will be laid between the generated strategy by Gasparo et al. [Nonmonotone algorithms for pattern search methods, Numer. Algorithms 28 (2001), pp. 171–186] and Ahookhosh and Amini [An efficient nonmonotone trust-region method for unconstrained optimization, Numer. Algorithms 59 (2012), pp. 523–540]. Reported are numerical results of the proposed algorithm for which the global convergence is established. Taylor & Francis 2017-12-19 /pmc/articles/PMC6235546/ /pubmed/30487705 http://dx.doi.org/10.1080/00207160.2017.1413552 Text en © 2017 Informa UK Limited, trading as Taylor & Francis Group |
spellingShingle | Original Article Amini, Keyvan Kimiaei, Morteza Khotanlou, Hassan A non-monotone pattern search approach for systems of nonlinear equations |
title | A non-monotone pattern search approach for systems of nonlinear equations |
title_full | A non-monotone pattern search approach for systems of nonlinear equations |
title_fullStr | A non-monotone pattern search approach for systems of nonlinear equations |
title_full_unstemmed | A non-monotone pattern search approach for systems of nonlinear equations |
title_short | A non-monotone pattern search approach for systems of nonlinear equations |
title_sort | non-monotone pattern search approach for systems of nonlinear equations |
topic | Original Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6235546/ https://www.ncbi.nlm.nih.gov/pubmed/30487705 http://dx.doi.org/10.1080/00207160.2017.1413552 |
work_keys_str_mv | AT aminikeyvan anonmonotonepatternsearchapproachforsystemsofnonlinearequations AT kimiaeimorteza anonmonotonepatternsearchapproachforsystemsofnonlinearequations AT khotanlouhassan anonmonotonepatternsearchapproachforsystemsofnonlinearequations AT aminikeyvan nonmonotonepatternsearchapproachforsystemsofnonlinearequations AT kimiaeimorteza nonmonotonepatternsearchapproachforsystemsofnonlinearequations AT khotanlouhassan nonmonotonepatternsearchapproachforsystemsofnonlinearequations |