Simultaneous Subgradient Algorithms for the Generalized Split Variational Inclusion Problem in Hilbert Spaces. (4th March 2017)

• Record Type: Journal Article
• Authors: Chuang, Chih-Sheng
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 3(2017)
• Page Start: 306
• Page End: 326
• Publication Date: 2017-03-04
• Subjects: Split equality problem -- split feasibility problem -- subgradient method -- variational inclusion problem; 49J53 -- 65K10 -- 49M37 -- 90C25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1233120
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we study the generalized split variational inclusion problem. For this purpose, motivated by the projected Landweber algorithm for the split equality problem, we first present a simultaneous subgradient extragradient algorithm and give related convergence theorems for the proposed algorithm. Next, motivated by the alternating CQ-algorithm for the split equality problem, we propose another simultaneous subgradient extragradient algorithm to study the general split variational inclusion problem. As applications, we consider the split equality problem, split feasibility problem, split variational inclusion problem, and variational inclusion problem in Hilbert spaces.