Generalized Halpern-type forward–backward splitting methods for convex minimization problems with application to image restoration problems. (2nd August 2020)

• Record Type: Journal Article
• Authors: Kitkuan, Duangkamon; Kumam, Poom; Martínez-Moreno, Juan
• Is Part Of: Optimization. Volume 69:Number 7/8(2020)
• Page Start: 1557
• Page End: 1581
• Publication Date: 2020-08-02
• Subjects: Forward–backward splitting method -- inclusion problem -- convex minimization problem -- monotone operator -- Hilbert spaces; 47H20 -- 49M20 -- 49M25 -- 49M27 -- 47J25 -- 47H05; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1646742
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this work, our interest is to investigate the monotone inclusion problem in the framework of real Hilbert spaces. For solving the inclusion problem, we propose a composite iteration for approximating a zero of sum of two operators. We prove its strong convergence under some mild conditions. Finally, we provide a number of applications to convex minimization and image restoration problems including numerical experiments to support our main theorem.