A self adaptive inertial algorithm for solving split variational inclusion and fixed point problems with applications

• Published in: Journal of industrial and management optimization Vol. 18; no. 1; pp. 239 - 265
• Main Authors: Alakoya, Timilehin Opeyemi, Jolaoso, Lateef Olakunle, Mewomo, Oluwatosin Temitope
• Format: Journal Article
• Language: English
• Published: Springfield American Institute of Mathematical Sciences 01.01.2022
• Subjects: Algorithms; Hilbert space; Iterative methods; Mapping; Optimization; Split variational inclusion problems; quasi-nonexpansive mappings; inertia; k-demicontractive mappings; strong convergence
• ISSN: 1553-166X; 1547-5816; 1553-166X
• DOI: 10.3934/jimo.2020152

We propose a general iterative scheme with inertial term and self-adaptive stepsize for approximating a common solution of Split Variational Inclusion Problem (SVIP) and Fixed Point Problem (FPP) for a quasi-nonexpansive mapping in real Hilbert spaces. We prove that our iterative scheme converges strongly to a common solution of SVIP and FPP for a quasi-nonexpansive mapping, which is also a solution of a certain optimization problem related to a strongly positive bounded linear operator. We apply our proposed algorithm to the problem of finding an equilibrium point with minimal cost of production for a model in industrial electricity production. Numerical results are presented to demonstrate the efficiency of our algorithm in comparison with some other existing algorithms in the literature.