Strong convergence of an inertial algorithm for maximal monotone inclusions with applications

Abstract An inertial iterative algorithm is proposed for approximating a solution of a maximal monotone inclusion in a uniformly convex and uniformly smooth real Banach space. The sequence generated by the algorithm is proved to converge strongly to a solution of the inclusion. Moreover, the theorem...

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Autores principales:	C. E. Chidume, A. Adamu, M. O. Nnakwe
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2020
Materias:	Nonlinear equations Monotone maps Zeros Optimization Hammerstein equation Strong convergence Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
Acceso en línea:	https://doaj.org/article/e612e857553340809dc734d4812d1e30
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spelling	oai:doaj.org-article:e612e857553340809dc734d4812d1e302021-12-02T11:09:49ZStrong convergence of an inertial algorithm for maximal monotone inclusions with applications10.1186/s13663-020-00680-21687-1812https://doaj.org/article/e612e857553340809dc734d4812d1e302020-08-01T00:00:00Zhttp://link.springer.com/article/10.1186/s13663-020-00680-2https://doaj.org/toc/1687-1812Abstract An inertial iterative algorithm is proposed for approximating a solution of a maximal monotone inclusion in a uniformly convex and uniformly smooth real Banach space. The sequence generated by the algorithm is proved to converge strongly to a solution of the inclusion. Moreover, the theorem proved is applied to approximate a solution of a convex optimization problem and a solution of a Hammerstein equation. Furthermore, numerical experiments are given to compare, in terms of CPU time and number of iterations, the performance of the sequence generated by our algorithm with the performance of the sequences generated by three recent inertial type algorithms for approximating zeros of maximal monotone operators. In addition, the performance of the sequence generated by our algorithm is compared with the performance of a sequence generated by another recent algorithm for approximating a solution of a Hammerstein equation. Finally, a numerical example is given to illustrate the implementability of our algorithm for approximating a solution of a convex optimization problem.C. E. ChidumeA. AdamuM. O. NnakweSpringerOpenarticleNonlinear equationsMonotone mapsZerosOptimizationHammerstein equationStrong convergenceApplied mathematics. Quantitative methodsT57-57.97AnalysisQA299.6-433ENFixed Point Theory and Applications, Vol 2020, Iss 1, Pp 1-22 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Nonlinear equations Monotone maps Zeros Optimization Hammerstein equation Strong convergence Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433
spellingShingle	Nonlinear equations Monotone maps Zeros Optimization Hammerstein equation Strong convergence Applied mathematics. Quantitative methods T57-57.97 Analysis QA299.6-433 C. E. Chidume A. Adamu M. O. Nnakwe Strong convergence of an inertial algorithm for maximal monotone inclusions with applications
description	Abstract An inertial iterative algorithm is proposed for approximating a solution of a maximal monotone inclusion in a uniformly convex and uniformly smooth real Banach space. The sequence generated by the algorithm is proved to converge strongly to a solution of the inclusion. Moreover, the theorem proved is applied to approximate a solution of a convex optimization problem and a solution of a Hammerstein equation. Furthermore, numerical experiments are given to compare, in terms of CPU time and number of iterations, the performance of the sequence generated by our algorithm with the performance of the sequences generated by three recent inertial type algorithms for approximating zeros of maximal monotone operators. In addition, the performance of the sequence generated by our algorithm is compared with the performance of a sequence generated by another recent algorithm for approximating a solution of a Hammerstein equation. Finally, a numerical example is given to illustrate the implementability of our algorithm for approximating a solution of a convex optimization problem.
format	article
author	C. E. Chidume A. Adamu M. O. Nnakwe
author_facet	C. E. Chidume A. Adamu M. O. Nnakwe
author_sort	C. E. Chidume
title	Strong convergence of an inertial algorithm for maximal monotone inclusions with applications
title_short	Strong convergence of an inertial algorithm for maximal monotone inclusions with applications
title_full	Strong convergence of an inertial algorithm for maximal monotone inclusions with applications
title_fullStr	Strong convergence of an inertial algorithm for maximal monotone inclusions with applications
title_full_unstemmed	Strong convergence of an inertial algorithm for maximal monotone inclusions with applications
title_sort	strong convergence of an inertial algorithm for maximal monotone inclusions with applications
publisher	SpringerOpen
publishDate	2020
url	https://doaj.org/article/e612e857553340809dc734d4812d1e30
work_keys_str_mv	AT cechidume strongconvergenceofaninertialalgorithmformaximalmonotoneinclusionswithapplications AT aadamu strongconvergenceofaninertialalgorithmformaximalmonotoneinclusionswithapplications AT monnakwe strongconvergenceofaninertialalgorithmformaximalmonotoneinclusionswithapplications
_version_	1718396202723049472

Strong convergence of an inertial algorithm for maximal monotone inclusions with applications

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