Inertial relaxed CQ algorithm for split feasibility problems with non-Lipschitz gradient operators. (4th May 2023)

• Record Type: Journal Article
• Authors: Ma, Xiaojun; Liu, Hongwei
• Is Part Of: Optimization. Volume 72:Number 5(2023)
• Page Start: 1239
• Page End: 1260
• Publication Date: 2023-05-04
• Subjects: CQ algorithm -- split feasibility problem -- weak convergence -- non-Lipschitz mapping; 47J20 -- 65K05 -- 65K10 -- 47J25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.2010077
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we propose a new inertial relaxed CQ algorithm for solving split feasibility problems in Hilbert spaces. The main advantages of the proposed algorithm are that the introduced stepsize is bounded away from zero and relaxation parameter sequences imposed on the stepsize itself are removed. These features help accelerate our method. Also, a weak convergence theorem for our method is established without Lipschitz continuous and firmly-nonexpasive conditions of split feasibility problem related gradient and projection mappings, respectively. As an application, we consider multiple-sets split feasiblity problems. Finally, some preliminary numerical experiments are provided for illustration and comparison.