Outer perturbations of a projection method and two approximation methods for the split equality problem. (2nd September 2018)

• Record Type: Journal Article
• Authors: Dong, Qiao-Li; Li, Xiao-Huan; He, Songnian
• Is Part Of: Optimization. Volume 67:Number 9(2018)
• Page Start: 1429
• Page End: 1446
• Publication Date: 2018-09-02
• Subjects: Split equality problem -- projection algorithm -- relaxed projection algorithm -- Halpern iteration method -- outer perturbation -- outer approximation method; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1474470
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this article, we first present a projection method with outer perturbations for the split equality problem (SEP) and establish its weak convergence. Then combining the proposed projection method with the outer approximation method and Halpern iteration method, we introduce two approximation methods to solve the SEP, where the two closed convex sets are both level sets of convex functions. Finally, a preliminary experiment presented compares the approximation methods and a relaxed projection method.