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
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ISSN0163-0563
1532-2467
DOI10.1080/01630563.2021.2006692

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Summary: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.
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ISSN:0163-0563
1532-2467
DOI:10.1080/01630563.2021.2006692