Strong convergence of two algorithms for the split feasibility problem in Banach spaces. (3rd October 2018)

• Record Type: Journal Article
• Authors: Wang, Fenghui
• Is Part Of: Optimization. Volume 67:Number 10(2018)
• Page Start: 1649
• Page End: 1660
• Publication Date: 2018-10-03
• Subjects: Split feasibility problem -- Bregman projection -- metric projection -- uniformly convex -- smooth -- duality mapping; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1483365
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we consider the split feasibility problem in Banach spaces. By converting it to an equivalent null-point problem, we propose two iterative algorithms, which are new even in Hilbert spaces. The parameter in one algorithm is chosen in such a way that no priori knowledge of the operator norms is required. It is shown that these two algorithms are strongly convergent provided that the involved Banach spaces are smooth and uniformly convex. Finally, we conduct numerical experiments to support the validity of the obtained results.