Modified Viscosity Subgradient Extragradient-Like Algorithms for Solving Monotone Variational Inequalities Problems

Variational inequality theory is an effective tool for engineering, economics, transport and mathematical optimization. Some of the approaches used to resolve variational inequalities usually involve iterative techniques. In this article, we introduce a new modified viscosity-type extragradient meth...

Full description

Bibliographic Details
Main Authors:	Nopparat Wairojjana, Mudasir Younis, Habib ur Rehman, Nuttapol Pakkaranang, Nattawut Pholasa
Format:	Article
Language:	English
Published:	MDPI AG 2020-10-01
Series:	Axioms
Subjects:	projection methods strong convergence extragradient method monotone mapping variational inequalities
Online Access:	https://www.mdpi.com/2075-1680/9/4/118

id	doaj-a03ba9baad864dedbb27866a0c9f3ca9
record_format	Article
spelling	doaj-a03ba9baad864dedbb27866a0c9f3ca92020-11-25T03:57:32ZengMDPI AGAxioms2075-16802020-10-01911811810.3390/axioms9040118Modified Viscosity Subgradient Extragradient-Like Algorithms for Solving Monotone Variational Inequalities ProblemsNopparat Wairojjana0Mudasir Younis1Habib ur Rehman2Nuttapol Pakkaranang3Nattawut Pholasa4Applied Mathematics Program, Faculty of Science and Technology, Valaya Alongkorn Rajabhat University under the Royal Patronage (VRU), 1 Moo 20 Phaholyothin Road, Klong Neung, Klong Luang, Pathumthani 13180, ThailandDepartment of Applied Mathematics, UIT-Rajiv Gandhi Technological University (University of Technology of M.P.), Bhopal 462033, IndiaDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok 10140, ThailandSchool of Science, University of Phayao, Phayao 56000, ThailandVariational inequality theory is an effective tool for engineering, economics, transport and mathematical optimization. Some of the approaches used to resolve variational inequalities usually involve iterative techniques. In this article, we introduce a new modified viscosity-type extragradient method to solve monotone variational inequalities problems in real Hilbert space. The result of the strong convergence of the method is well established without the information of the operator’s Lipschitz constant. There are proper mathematical studies relating our newly designed method to the currently state of the art on several practical test problems.https://www.mdpi.com/2075-1680/9/4/118projection methodsstrong convergenceextragradient methodmonotone mappingvariational inequalities
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Nopparat Wairojjana Mudasir Younis Habib ur Rehman Nuttapol Pakkaranang Nattawut Pholasa
spellingShingle	Nopparat Wairojjana Mudasir Younis Habib ur Rehman Nuttapol Pakkaranang Nattawut Pholasa Modified Viscosity Subgradient Extragradient-Like Algorithms for Solving Monotone Variational Inequalities Problems Axioms projection methods strong convergence extragradient method monotone mapping variational inequalities
author_facet	Nopparat Wairojjana Mudasir Younis Habib ur Rehman Nuttapol Pakkaranang Nattawut Pholasa
author_sort	Nopparat Wairojjana
title	Modified Viscosity Subgradient Extragradient-Like Algorithms for Solving Monotone Variational Inequalities Problems
title_short	Modified Viscosity Subgradient Extragradient-Like Algorithms for Solving Monotone Variational Inequalities Problems
title_full	Modified Viscosity Subgradient Extragradient-Like Algorithms for Solving Monotone Variational Inequalities Problems
title_fullStr	Modified Viscosity Subgradient Extragradient-Like Algorithms for Solving Monotone Variational Inequalities Problems
title_full_unstemmed	Modified Viscosity Subgradient Extragradient-Like Algorithms for Solving Monotone Variational Inequalities Problems
title_sort	modified viscosity subgradient extragradient-like algorithms for solving monotone variational inequalities problems
publisher	MDPI AG
series	Axioms
issn	2075-1680
publishDate	2020-10-01
description	Variational inequality theory is an effective tool for engineering, economics, transport and mathematical optimization. Some of the approaches used to resolve variational inequalities usually involve iterative techniques. In this article, we introduce a new modified viscosity-type extragradient method to solve monotone variational inequalities problems in real Hilbert space. The result of the strong convergence of the method is well established without the information of the operator’s Lipschitz constant. There are proper mathematical studies relating our newly designed method to the currently state of the art on several practical test problems.
topic	projection methods strong convergence extragradient method monotone mapping variational inequalities
url	https://www.mdpi.com/2075-1680/9/4/118
work_keys_str_mv	AT nopparatwairojjana modifiedviscositysubgradientextragradientlikealgorithmsforsolvingmonotonevariationalinequalitiesproblems AT mudasiryounis modifiedviscositysubgradientextragradientlikealgorithmsforsolvingmonotonevariationalinequalitiesproblems AT habiburrehman modifiedviscositysubgradientextragradientlikealgorithmsforsolvingmonotonevariationalinequalitiesproblems AT nuttapolpakkaranang modifiedviscositysubgradientextragradientlikealgorithmsforsolvingmonotonevariationalinequalitiesproblems AT nattawutpholasa modifiedviscositysubgradientextragradientlikealgorithmsforsolvingmonotonevariationalinequalitiesproblems
_version_	1724460307210829824

Modified Viscosity Subgradient Extragradient-Like Algorithms for Solving Monotone Variational Inequalities Problems

Similar Items