On solving proximal split feasibility problems and applications. (English) Zbl 1394.47071

Witthayarat, Uamporn; Cho, Yeol Je; Cholamjiak, Prasit

Ann. Funct. Anal. 9, No. 1, 111-122 (2018).

Summary: We study the problem of proximal split feasibility of two objective convex functions in Hilbert spaces. We prove that, under suitable conditions, certain strong convergence theorems of the Halpern-type algorithm present solutions to the proximal split feasibility problem. Finally, we provide some related applications as well as numerical experiments.

MSC:

47J25	Iterative procedures involving nonlinear operators
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H05	Monotone operators and generalizations

Keywords:

split feasibility problem; strong convergence; Halpern-type algorithm; proximity operator; strong convergence