Two New Inertial Algorithms for Solving Variational Inequalities in Reflexive Banach Spaces

The purpose of this paper is to introduce and analyze two inertial algorithms with self-adaptive stepsizes for solving variational inequalities in reflexive Banach spaces. Our algorithms are based on inertial hybrid and shrinking projection methods. Knowledge of the Lipschitz constant of the cost op...

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Published inNumerical functional analysis and optimization Vol. 42; no. 16; pp. 1954 - 1984
Main Authors Reich, Simeon, Tuyen, Truong Minh, Sunthrayuth, Pongsakorn, Cholamjiak, Prasit
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 30.03.2022
Taylor & Francis Ltd
Subjects
Adaptive algorithms
Algorithms
Banach spaces
Bregman projection
extragradient method
Hilbert space
Inequalities
Legendre function
Mathematical analysis
Operators (mathematics)
reflexive banach space
strong convergence
Online AccessGet full text
ISSN0163-0563
1532-2467
DOI10.1080/01630563.2021.2006692

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Abstract The purpose of this paper is to introduce and analyze two inertial algorithms with self-adaptive stepsizes for solving variational inequalities in reflexive Banach spaces. Our algorithms are based on inertial hybrid and shrinking projection methods. Knowledge of the Lipschitz constant of the cost operator is not required. Under appropriate conditions, the strong convergence of the algorithms is established. We also present several numerical experiments which bring out the efficiency and the advantages of the proposed algorithms. Our work provides extensions of many known results from Hilbert spaces to reflexive Banach spaces.
AbstractList The purpose of this paper is to introduce and analyze two inertial algorithms with self-adaptive stepsizes for solving variational inequalities in reflexive Banach spaces. Our algorithms are based on inertial hybrid and shrinking projection methods. Knowledge of the Lipschitz constant of the cost operator is not required. Under appropriate conditions, the strong convergence of the algorithms is established. We also present several numerical experiments which bring out the efficiency and the advantages of the proposed algorithms. Our work provides extensions of many known results from Hilbert spaces to reflexive Banach spaces.
Author Sunthrayuth, Pongsakorn
Tuyen, Truong Minh
Cholamjiak, Prasit
Reich, Simeon
Author_xml – sequence: 1
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  surname: Reich
  fullname: Reich, Simeon
  organization: Department of Mathematics, The Technion - Israel Institute of Technology
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  givenname: Truong Minh
  surname: Tuyen
  fullname: Tuyen, Truong Minh
  organization: Department of Mathematics and Informatics, Thai Nguyen University of Sciences
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  givenname: Pongsakorn
  surname: Sunthrayuth
  fullname: Sunthrayuth, Pongsakorn
  organization: Faculty of Science and Technology, Department of Mathematics and Computer Science, Rajamangala University of Technology Thanyaburi (RMUTT)
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  givenname: Prasit
  surname: Cholamjiak
  fullname: Cholamjiak, Prasit
  organization: School of Science, University of Phayao
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Snippet The purpose of this paper is to introduce and analyze two inertial algorithms with self-adaptive stepsizes for solving variational inequalities in reflexive...
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StartPage 1954
SubjectTerms Adaptive algorithms
Algorithms
Banach spaces
Bregman projection
extragradient method
Hilbert space
Inequalities
Legendre function
Mathematical analysis
Operators (mathematics)
reflexive banach space
strong convergence
Title Two New Inertial Algorithms for Solving Variational Inequalities in Reflexive Banach Spaces
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