Modified proximal point algorithms involving convex combination technique for solving minimization problems with convergence analysis. (2nd August 2020)

• Record Type: Journal Article
• Authors: Wairojjana, Nopparat; Pakkaranang, Nuttapol; Uddin, Izhar; Kumam, Poom; Awwal, Aliyu Muhammed
• Is Part Of: Optimization. Volume 69:Number 7/8(2020)
• Page Start: 1655
• Page End: 1680
• Publication Date: 2020-08-02
• Subjects: Proximal point algorithm -- asymptotically nonexpansive mapping -- Hadamard space -- minimization problem -- iteration process; 47H09 -- 47H10 -- 65K10 -- 65K15; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1657115
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we are interested in solving minimization problem and common fixed point problem of finite family consisting asymptotically nonexpansive mappings in Hadamard spaces. For finding common solutions of their problems, we introduce a new modified proximal point algorithm involving convex combination technique. Under suitable conditions, Δ-convergence and strong convergence theorems are proved. Furthermore, we provide some numerical examples which show the efficiency and implementation of the proposed algorithm as well as show computational overview by comparing it with previously known algorithms.