Two New Inertial Algorithms for Solving Variational Inequalities in Reflexive Banach Spaces. (30th March 2022)

• Record Type: Journal Article
• Authors: Reich, Simeon; Tuyen, Truong Minh; Sunthrayuth, Pongsakorn; Cholamjiak, Prasit
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 16(2021)
• Page Start: 1954
• Page End: 1984
• Publication Date: 2022-03-30
• Subjects: Bregman projection -- extragradient method -- Legendre function -- reflexive banach space -- strong convergence; 47H09 -- 47H10 -- 47J25 -- 47J05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.2006692
• Languages: English
• ISSNs: 0163-0563

Abstract

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.