Proximal type algorithms involving linesearch and inertial technique for split variational inclusion problem in hilbert spaces with applications. (2nd December 2019)

• Record Type: Journal Article
• Authors: Kesornprom, Suparat; Cholamjiak, Prasit
• Is Part Of: Optimization. Volume 68:Number 12(2019)
• Page Start: 2369
• Page End: 2395
• Publication Date: 2019-12-02
• Subjects: Split variational inclusion problem -- inertial technique -- linesearch -- proximal algorithm -- hilbert spaces; 49J40 -- 47J20 -- 35A15 -- 65K10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1638389
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In convex optimization, numerous problems in applied sciences can be modelled as the split variational inclusion problem (SVIP). In this connection, we aim to design new and efficient proximal type algorithms which are based on the inertial technique and the linesearches terminology. We then discuss its convergence under some suitable conditions without the assumption on the operator norm. We also apply our main result to the split minimization problem, the split feasibility problem, the relaxed split feasibility problem and the linear inverse problem. Finally, we provide some numerical experiments and comparisons to these problems. The obtained result mainly improves the recent results investigated by Chuang.