The Modified Viscosity Approximation Method with Inertial Technique and Forward–Backward Algorithm for Convex Optimization Model

Adisak Hanjing, Limpapat Bussaban and Suthep Suantai
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Adisak Hanjing: Department of Science and Mathematics, Rajamangala University of Technology Isan Surin Campus, Surin 32000, Thailand
Limpapat Bussaban: Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
Suthep Suantai: Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Mathematics, 2022, vol. 10, issue 7, 1-16

Abstract: In this paper, we propose a new accelerated algorithm for finding a common fixed point of nonexpansive operators, and then, a strong convergence result of the proposed method is discussed and analyzed in real Hilbert spaces. As an application, we create a new accelerated viscosity forward–backward method (AVFBM) for solving nonsmooth optimization problems of the sum of two objective functions in real Hilbert spaces, and the strong convergence of AVFBM to a minimizer of the sum of two convex functions is established. We also present the application and simulated results of AVFBM for image restoration and data classification problems.

Keywords: Hilbert space; common fixed points; viscosity forward–backward algorithm; convergence theorems; convex optimization model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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