A general algorithm for multiple-sets split feasibility problem involving resolvents and Bregman mappings. (1st February 2018)

• Record Type: Journal Article
• Authors: Raeisi, M.; Zamani Eskandani, G.; Eslamian, M.
• Is Part Of: Optimization. Volume 67:Number 2(2018)
• Page Start: 309
• Page End: 327
• Publication Date: 2018-02-01
• Subjects: Bregman projection -- duality mapping -- multi-valued Bregman relatively nonexpansive mappings -- multiple-sets split feasibility problem; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1396603
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, by using Bregman distance, we introduce a new iterative process involving products of resolvents of maximal monotone operators for approximating a common element of the set of common fixed points of a finite family of multi-valued Bregman relatively nonexpansive mappings and the solution set of the multiple-sets split feasibility problem and common zeros of maximal monotone operators. We derive a strong convergence theorem of the proposed iterative algorithm under appropriate situations. Finally, we mention several corollaries and two applications of our algorithm.