Remark on the Successive Projection Algorithm for the Multiple-Sets Split Feasibility Problem. (2nd December 2017)

• Record Type: Journal Article
• Authors: Qu, Biao; Chang, Hanxiao
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 12(2017)
• Page Start: 1614
• Page End: 1623
• Publication Date: 2017-12-02
• Subjects: Convergence -- multiple-sets split feasibility problem -- relaxed successive projection algorithm; 90C30 -- 90C25 -- 65K10; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1369109
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: Recently, assuming that the metric projection onto a closed convex set is easily calculated, Liu et al. ( Numer. Func. Anal. Opt. 35:1459–1466, 2014) presented a successive projection algorithm for solving the multiple-sets split feasibility problem (MSFP). However, in some cases it is impossible or needs too much work to exactly compute the metric projection. The aim of this remark is to give a modification to the successive projection algorithm. That is, we propose a relaxed successive projection algorithm, in which the metric projections onto closed convex sets are replaced by the metric projections onto halfspaces. Clearly, the metric projection onto a halfspace may be directly calculated. So, the relaxed successive projection algorithm is easy to implement. Its theoretical convergence results are also given.