The Strongly Convergent Relaxed Alternating CQ Algorithms for the Split Equality Problem in Hilbert Spaces. (11th June 2021)

• Record Type: Journal Article
• Authors: Gao, Fugen; Liu, Xiaoxiao
• Is Part Of: Numerical functional analysis and optimization. Volume 42:Number 8(2021)
• Page Start: 902
• Page End: 918
• Publication Date: 2021-06-11
• Subjects: Coupled fixed -- point equation -- relaxed alternating method -- split equality problem; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.1933522
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Recently, Moudafi introduced the split equality problem (SEP): find x ∈ C, y ∈ Q such that Ax = By . In this paper, we show that finding a solution of the SEP is equivalent to finding a solution of a coupled fixed-point equation which is an extension of the coupled equation proposed by Yu and Wang. Based on this coupled fixed-point equation, we propose two new relaxed alternating algorithms for the SEP, and we prove that the first relaxed algorithm is weakly convergent and the second is strongly convergent.