Modified Tseng’s Method with Inertial Viscosity Type for Solving Inclusion Problems and Its Application to Image Restoration Problems

Nattakarn Kaewyong and Kanokwan Sitthithakerngkiet
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Nattakarn Kaewyong: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand
Kanokwan Sitthithakerngkiet: Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand

Mathematics, 2021, vol. 9, issue 10, 1-15

Abstract: In this paper, we study a monotone inclusion problem in the framework of Hilbert spaces. (1) We introduce a new modified Tseng’s method that combines inertial and viscosity techniques. Our aim is to obtain an algorithm with better performance that can be applied to a broader class of mappings. (2) We prove a strong convergence theorem to approximate a solution to the monotone inclusion problem under some mild conditions. (3) We present a modified version of the proposed iterative scheme for solving convex minimization problems. (4) We present numerical examples that satisfy the image restoration problem and illustrate our proposed algorithm’s computational performance.

Keywords: inertial algorithm; Tseng’s method; forward-backward algorithm; monotone inclusion problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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