Contraction of the proximal mapping and applications to the equilibrium problem. (4th March 2017)

• Record Type: Journal Article
• Authors: Trinh, Ngoc Hai
• Is Part Of: Optimization. Volume 66:Number 3(2017)
• Page Start: 381
• Page End: 396
• Publication Date: 2017-03-04
• Subjects: Proximal mapping -- equilibrium problem -- variational inequality problem -- fixed-point problem -- contractive mapping -- nonexpansive mapping; 90C33 -- 65K10 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1269764
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract: In this paper, we introduce a new definition of Lipschitz-type continuity of a bifunction. Using this definition, we prove the contraction of the proximal mapping and apply it to the equilibrium problem over the fixed-point set of a nonexpansive mapping. We present a new algorithm for this problem. Under classical conditions, the convergence of the algorithm is proved. Finally, we present some numerical results for the proposed algorithm.