title: Modified projection algorithms for solving the split equality problems.
abstract: The split equality problem (SEP) has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Byrne and Moudafi (2013) proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively and performs an additional projection step onto two half-spaces in each iteration. We further propose a relaxation scheme for the self-adaptive projection algorithm by using projections onto half-spaces instead of those onto the original convex sets, which is much more practical. Weak convergence results for both algorithms are analyzed.
authors.affiliation: College of Science, Civil Aviation University of China, Tianjin 300300, China.
authors.forename: Qiao-Li
authors.initials: QL
authors.lastname: Dong
authors.affiliation: College of Science, Civil Aviation University of China, Tianjin 300300, China.
authors.forename: Songnian
authors.initials: S
authors.lastname: He
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical