New algorithms for the split common null point problem. (3rd June 2021)

• Record Type: Journal Article
• Authors: Tang, Yan
• Is Part Of: Optimization. Volume 70:Number 5/6(2021)
• Page Start: 1141
• Page End: 1160
• Publication Date: 2021-06-03
• Subjects: Split common null point problem -- monotone mapping -- weak convergence -- strong convergence; 65K10 -- 65K05 -- 47H10 -- 47L25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1782908
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: Two new iterative algorithms are introduced for solving the split common null point problem (SCNPP). The first algorithm is shown to converge weakly and the second is shown to converge strongly to a solution of SCNPP in a Hilbert space. The algorithms are forward methods (i.e, involving no computation of the resolvent of a monotone operator). Another feature of the algorithms is that the selection of the step-sizes does not need prior knowledge of operator norms. Numerical experiments are presented to illustrate the performance of the algorithms.