On a system of monotone variational inclusion problems with fixed-point constraint

• Published in: Journal of inequalities and applications Vol. 2022; no. 1; pp. 1 - 30
• Main Authors: Alakoya, Timilehin O., Uzor, Victor A., Mewomo, Oluwatosin T., Yao, Jen-Chih
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 27.04.2022; Springer Nature B.V; SpringerOpen
• Subjects: Algorithms; Analysis; Applications of Mathematics; Control theory; Data compression; Fixed-point problem; Hilbert space; Inertial technique; Inverse problems; Iterative methods; Mathematics; Mathematics and Statistics; Medical research; Optimization; Quasipseudocontractions; Radiation therapy; Self-adaptive step size; Signal processing; System of monotone variational inclusion problems; Self-adaptive step size; 65K15; Fixed-point problem; System of monotone variational inclusion problems; 90C33; Quasipseudocontractions; Inertial technique; 47J25; 65J15
• DOI: 10.1186/s13660-022-02782-4
• ISSN: 1029-242X; 1025-5834

In this paper, we study the problem of finding the solution of the system of monotone variational inclusion problems recently introduced by Chang et al. (Optimization 70(12):2511–2525, 2020 ) with the constraint of a fixed-point set of quasipseudocontractive mappings. We propose a new iterative method that employs an inertial technique with self-adaptive step size for approximating the solution of the problem in Hilbert spaces and prove a strong-convergence result for the proposed method under more relaxed conditions. Moreover, we apply our results to study related optimization problems. Finally, we present some numerical experiments to demonstrate the performance of our proposed method, compare it with a related method as well as experiment on the dependency of the key parameters on the performance of our method.