Relaxed Inertial Tseng’s Type Method for Solving the Inclusion Problem with Application to Image Restoration

Jamilu Abubakar, Poom Kumam, Abdulkarim Hassan Ibrahim and Anantachai Padcharoen
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Jamilu Abubakar: Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand
Poom Kumam: Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand
Abdulkarim Hassan Ibrahim: Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand
Anantachai Padcharoen: Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University, Chanthaburi 22000, Thailand

Mathematics, 2020, vol. 8, issue 5, 1-19

Abstract: The relaxed inertial Tseng-type method for solving the inclusion problem involving a maximally monotone mapping and a monotone mapping is proposed in this article. The study modifies the Tseng forward-backward forward splitting method by using both the relaxation parameter, as well as the inertial extrapolation step. The proposed method follows from time explicit discretization of a dynamical system. A weak convergence of the iterates generated by the method involving monotone operators is given. Moreover, the iterative scheme uses a variable step size, which does not depend on the Lipschitz constant of the underlying operator given by a simple updating rule. Furthermore, the proposed algorithm is modified and used to derive a scheme for solving a split feasibility problem. The proposed schemes are used in solving the image deblurring problem to illustrate the applicability of the proposed methods in comparison with the existing state-of-the-art methods.

Keywords: variational inclusion problem; Lipschitz-type conditions; forward-backward method; zero point; image restoration; maximal monotone operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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