Modified Hybrid Steepest Method for the Split Feasibility Problem in Image Recovery of Inverse Problems. (3rd April 2017)

• Record Type: Journal Article
• Authors: Sitthithakerngkiet, Kanokwan; Deepho, Jitsupa; Kumam, Poom
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 4(2017)
• Page Start: 507
• Page End: 522
• Publication Date: 2017-04-03
• Subjects: CQ algorithm -- fixed point -- hybrid steepest method -- inverse problems -- split feasibility problem -- variational inequality -- viscosity method; 47H10 -- 35A15 -- 35D40 -- 65K10 -- 49J40; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1287084
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, we regard the CQ algorithm as a fixed point algorithm for averaged mapping, and also try to study the split feasibility problem by the following hybrid steepest method; where { α n }⊂(0, 1). It is noted that Xu's original iterative method can conclude only weak convergence. Consequently, we obtain the sequence { x n } generated by our iteration method converges strongly to, where is the unique solution of the variational inequality Our result extends and improves the result of Xu, as shown in the literature, from weak to strong convergence theorems. Finally, in the last section, numerical examples for study behavior convergence analysis of this algorithm are obtained.