A Bregman subgradient extragradient method with self-adaptive technique for solving variational inequalities in reflexive Banach spaces. (9th December 2022)

• Record Type: Journal Article
• Authors: Jolaoso, L. O.; Oyewole, O.K.; Aremu, K.O.
• Is Part Of: Optimization. Volume 71:Number 13(2022)
• Page Start: 3835
• Page End: 3860
• Publication Date: 2022-12-09
• Subjects: Bregman distance -- variational inequalities -- self-adaptive stepsize -- extragradient method -- pseudomonotone operators; 47H09 -- 65K10 -- 90C25 -- 49J25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1925669
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we introduce a self-adaptive Bregman subgradient extragradient method for solving variational inequalities in the framework of a reflexive Banach space. The step-adaptive strategy avoids the difficult task of choosing a stepsize based on the Lipschitz constant of the cost function of the variational inequalities and improves the performance of the algorithm. Moreover, the use of the Bregman distance technique allows the consideration of a general feasible set for the problem. Under some suitable conditions, we prove some weak and strong convergence results for the sequence generated by the algorithm without prior knowledge of the Lipschitz constant. We further provide an application to contact problems and some numerical experiments to illustrate the performance of the algorithm.