Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces

In this paper, we introduce a new algorithm for solving pseudomonotone variational inequalities with a Lipschitz-type condition in a real Hilbert space. The algorithm is constructed around two algorithms: the subgradient extragradient algorithm and the inertial algorithm. The proposed algorithm uses...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Wairojjana Nopparat, Pakkaranang Nuttapol, Pholasa Nattawut
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	variational inequalities extragradient-like algorithm strong convergence theorem lipschitz continuity pseudomonotone mapping 65y05 65k15 68w10 47h05 47h10 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/b043747aed5749e58eaac5136b309188
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:b043747aed5749e58eaac5136b309188
record_format	dspace
spelling	oai:doaj.org-article:b043747aed5749e58eaac5136b3091882021-12-05T14:10:45ZStrong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces2391-466110.1515/dema-2021-0011https://doaj.org/article/b043747aed5749e58eaac5136b3091882021-05-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0011https://doaj.org/toc/2391-4661In this paper, we introduce a new algorithm for solving pseudomonotone variational inequalities with a Lipschitz-type condition in a real Hilbert space. The algorithm is constructed around two algorithms: the subgradient extragradient algorithm and the inertial algorithm. The proposed algorithm uses a new step size rule based on local operator information rather than its Lipschitz constant or any other line search scheme and functions without any knowledge of the Lipschitz constant of an operator. The strong convergence of the algorithm is provided. To determine the computational performance of our algorithm, some numerical results are presented.Wairojjana NopparatPakkaranang NuttapolPholasa NattawutDe Gruyterarticlevariational inequalitiesextragradient-like algorithmstrong convergence theoremlipschitz continuitypseudomonotone mapping65y0565k1568w1047h0547h10MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 110-128 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	variational inequalities extragradient-like algorithm strong convergence theorem lipschitz continuity pseudomonotone mapping 65y05 65k15 68w10 47h05 47h10 Mathematics QA1-939
spellingShingle	variational inequalities extragradient-like algorithm strong convergence theorem lipschitz continuity pseudomonotone mapping 65y05 65k15 68w10 47h05 47h10 Mathematics QA1-939 Wairojjana Nopparat Pakkaranang Nuttapol Pholasa Nattawut Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces
description	In this paper, we introduce a new algorithm for solving pseudomonotone variational inequalities with a Lipschitz-type condition in a real Hilbert space. The algorithm is constructed around two algorithms: the subgradient extragradient algorithm and the inertial algorithm. The proposed algorithm uses a new step size rule based on local operator information rather than its Lipschitz constant or any other line search scheme and functions without any knowledge of the Lipschitz constant of an operator. The strong convergence of the algorithm is provided. To determine the computational performance of our algorithm, some numerical results are presented.
format	article
author	Wairojjana Nopparat Pakkaranang Nuttapol Pholasa Nattawut
author_facet	Wairojjana Nopparat Pakkaranang Nuttapol Pholasa Nattawut
author_sort	Wairojjana Nopparat
title	Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces
title_short	Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces
title_full	Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces
title_fullStr	Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces
title_full_unstemmed	Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces
title_sort	strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in hilbert spaces
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/b043747aed5749e58eaac5136b309188
work_keys_str_mv	AT wairojjananopparat strongconvergenceinertialprojectionalgorithmwithselfadaptivestepsizeruleforpseudomonotonevariationalinequalitiesinhilbertspaces AT pakkaranangnuttapol strongconvergenceinertialprojectionalgorithmwithselfadaptivestepsizeruleforpseudomonotonevariationalinequalitiesinhilbertspaces AT pholasanattawut strongconvergenceinertialprojectionalgorithmwithselfadaptivestepsizeruleforpseudomonotonevariationalinequalitiesinhilbertspaces
_version_	1718371769379717120

Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces

Ejemplares similares