Ball-relaxed projection algorithms for multiple-sets split feasibility problem. (2nd December 2022)

• Record Type: Journal Article
• Authors: Taddele, Guash Haile; Kumam, Poom; Gebrie, Anteneh Getachew; Abubakar, Jamilu
• Is Part Of: Optimization. Volume 71:Number 12(2022)
• Page Start: 3571
• Page End: 3601
• Publication Date: 2022-12-02
• Subjects: Multiple-sets split feasibility problem -- strongly convex function -- Hilbert space -- relaxed CQ algorithm -- ball -- self-adaptive technique; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1905640
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: The multiple-sets split feasibility problem (MSSFP) requires finding a point closet to a family of closed convex sets in one space such that its image under a linear transformation will be closest to another family of closed convex sets in the image space. Motivated by the ball-relaxed projection algorithm proposed by Yu et al. for the split feasibility problem (SFP), in this paper, we introduce ball-relaxed projection algorithms for solving the MSSFP. Instead of the level sets or half-spaces, our algorithms require computing the orthogonal projections onto closed balls. We establish weak and strong convergence of the proposed algorithms to a solution of the MSSFP. Finally, we provide preliminary numerical experiments to show the efficiency and the implementation of our method.