Hybrid Moreau's Proximal Algorithms and Convergence Theorems for Minimization Problems in Hilbert Spaces with Applications. (10th December 2018)

• Record Type: Journal Article
• Authors: Chuang, Chih-Sheng
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 16(2018)
• Page Start: 1806
• Page End: 1832
• Publication Date: 2018-12-10
• Subjects: Projection -- proximal gradient algorithm -- split feasible problem -- strong convergence; 46B20 -- 46N10 -- 47H09; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1501382
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, motivated by Moreau's proximal algorithm, we give several algorithms and related weak and strong convergence theorems for minimization problems under suitable conditions. These algorithms and convergence theorems are different from the results in the literatures. Besides, we also study algorithms and convergence theorems for the split feasibility problem in real Hilbert spaces. Finally, we give numerical results for our main results.