A new self-adaptive method for the split equality common fixed-point problem of quasi-nonexpansive mappings. (3rd April 2021)

• Record Type: Journal Article
• Authors: Zhao, Jing; Hou, Dingfang; Wang, Xinglong
• Is Part Of: Optimization. Volume 70:Number 4(2021)
• Page Start: 805
• Page End: 826
• Publication Date: 2021-04-03
• Subjects: Split equality common fixed-point problem -- split feasibility problem -- quasi-nonexpansive mapping -- primal-dual algorithm -- weak convergence; 47H09 -- 47H10 -- 47J05 -- 54H25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1830400
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we introduce a new iterative algorithm from primal-dual methods for solving the split equality common fixed-point problem of quasi-nonexpansive mappings in real Hilbert space. Our algorithm includes the simultaneous iterative algorithm as special case which has been proposed by Moudafi and Al-Shemas for solving the split equality common fixed-point problem. We use a way of selecting the stepsizes such that the implementation of our algorithm does not need any prior information about bounded linear operator norms. It avoids the difficult task of estimating the operator norms. Under suitable conditions, we get the weak convergence of the proposed algorithm. The performance of the proposed algorithm is also illustrated by preliminary numerical experiments. The results presented in the paper improve and extend some corresponding results.