Regularization methods for accretive variational inequalities over the set of common fixed points of nonexpansive semigroups. (2nd August 2016)

• Record Type: Journal Article
• Authors: Thuy, Nguyen Thi Thu; Hieu, Pham Thanh; Strodiot, Jean Jacques
• Is Part Of: Optimization. Volume 65:Number 8(2016)
• Page Start: 1553
• Page End: 1567
• Publication Date: 2016-08-02
• Subjects: Regularization -- variational inequality -- common fixed point -- nonexpansive semigroup -- accretive mapping -- NST condition; 41A65 -- 47H17 -- 47H20; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1166501
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we introduce a regularization method based on the Browder–Tikhonov regularization method for solving a class of accretive variational inequalities over the set of common fixed points of a nonexpansive semigroup on a uniformly smooth Banach space. Three algorithms based on this regularization method are given and their strong convergence is studied. Finally, a finite-dimensional example is developed to illustrate the numerical behaviour of the algorithms.