Extragradient methods for nonsmooth equilibrium problems in Banach spaces. (1st November 2020)

• Record Type: Journal Article
• Authors: Iusem, Alfredo N.; Mohebbi, Vahid
• Is Part Of: Optimization. Volume 69:Number 11(2020)
• Page Start: 2383
• Page End: 2403
• Publication Date: 2020-11-01
• Subjects: Armijo linesearch -- equilibrium problem -- extragradient method -- Halpern regularization -- pseudomonotone bifunction; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1462808
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: We introduce and analyse the extragradient method for solving nonsmooth equilibrium problems in Banach spaces, which generalizes the extragradient method for variational inequalities. We prove weak convergence of the generated sequence to a solution of the equilibrium problem, under standard assumptions on the bifunction which defines the problem, akin to those required in the convergence analysis of the method, when applied to solving variational inequalities. Then, we propose a regularization procedure which ensures strong convergence of the generated sequence to a solution of the problem.