Convergence analysis and applications of the inertial algorithm solving inclusion problems

• Published in: Applied numerical mathematics Vol. 175; pp. 1 - 17
• Main Authors: Tang, Yan, Lin, Honghua, Gibali, Aviv, Je Cho, Yeol
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.05.2022
• Subjects: Fixed point; Forward-backward algorithm; Inertial technique; Monotone operator equation; Nonexpansive mapping; Inertial technique; Monotone operator equation; Forward-backward algorithm; Nonexpansive mapping; Fixed point
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2022.01.016

Nonlinear operator theory is an important area of nonlinear functional analysis. This area encompasses diverse nonlinear problems in many areas of mathematics, the physical sciences and engineering such as monotone operator equations, fixed point problems and more. In this work we are concern with the problem of finding a common solution of a monotone operator equation and fixed point of a nonexpansive mapping in real Hilbert spaces. Derived from dynamical systems, a simple inertial forward-backward splitting method for solving the problem is presented and analyzed under mild and standard assumptions. Some numerical examples in real-world and comparisons with related works, illustrate the theoretical advantages as well the potential applicability of the proposed scheme.