Inertial relaxed CQ algorithm for split feasibility problems with non-Lipschitz gradient operators

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.

Keywords:

• CQ algorithm
• split feasibility problem
• weak convergence
• non-Lipschitz mapping

Mathematics Subject Classifications:

• 47J20
• 65K05
• 65K10
• 47J25

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The second author was supported by National Natural Science Foundation of China [grant number 11801430].