Strong convergence of a hybrid steepest descent method for the split common fixed point problem. (2nd July 2016)

• Record Type: Journal Article
• Authors: Cegielski, Andrzej; Al-Musallam, Fadhel
• Is Part Of: Optimization. Volume 65:Number 7(2016)
• Page Start: 1463
• Page End: 1476
• Publication Date: 2016-07-02
• Subjects: Variational inequality problem -- fixed point -- quasi-nonexpansive operator -- approximately shrinking operator -- Landweber-type operator; 47H05 -- 47H09 -- 47H10 -- 65K15; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2016.1147038
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We study the convergence properties of an iterative method for a variational inequality defined on a solution set of the split common fixed point problem. The method involves Landweber-type operators related to the problem as well as their extrapolations in an almost cyclic way. The evaluation of these extrapolations does not require prior knowledge of the matrix norm. We prove the strong convergence under the assumption that the operators employed in the method are approximately shrinking.