TY - JOUR
T1 - A SELF ADAPTIVE INERTIAL ALGORITHM FOR SOLVING SPLIT VARIATIONAL INCLUSION AND FIXED POINT PROBLEMS WITH APPLICATIONS
AU - Alakoya, Timilehin Opeyemi
AU - Jolaoso, Lateef Olakunle
AU - Mewomoİ, Oluwatosin Temitope
N1 - Funding Information:
Acknowledgments. The authors sincerely thank the anonymous reviewer for his careful reading, constructive comments and fruitful suggestions that substantially improved the manuscript. The second author acknowledges with thanks the bursary and financial support from Department of Science and Innovation and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF COE-MaSS) Doctoral Bursary. The third author is supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903). Opinions expressed and
Publisher Copyright:
© 2022. All Rights Reserved.
PY - 2022/1
Y1 - 2022/1
N2 - 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.
AB - 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.
KW - Split variational inclusion problems
KW - inertia
KW - k-demicontractive mappings
KW - quasi-nonexpansive mappings
KW - strong convergence
UR - http://www.scopus.com/inward/record.url?scp=85123457871&partnerID=8YFLogxK
U2 - 10.3934/jimo.2020152
DO - 10.3934/jimo.2020152
M3 - Article
AN - SCOPUS:85123457871
SN - 1547-5816
VL - 18
SP - 239
EP - 265
JO - Journal of Industrial and Management Optimization
JF - Journal of Industrial and Management Optimization
IS - 1
ER -