Analysis of relaxed inertial method for non-convex mixed variational inequalities
Fixed Point Methods and Optimization, Volume 1, Issue 1, June 2024, Pages 1–16
CHIBUEZE CHRISTIAN OKEKE
School of Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa
ABDULMALIK USMAN BELLO
Mathematics Institute African University of Science and Technology, Abuja, Nigeria
Abstract
This paper extends inertial forward-backward-forward splitting method already studied by several authors for solving convex variational inequalities to solving non-convex mixed variational inequalities and obtain appropriate convergence results under some conditions. Next, we propose another inertial forward-backward-forward splitting method for which the inertial factor \(\theta\) is chosen in \([0, 1]\) with \(\theta = 1\) possible. As far as we know, the choice \(\theta = 1\) has not been considered before in the literature for inertial forward-backward-forward splitting method for solving non-convex mixed variational inequalities. Numerical illustrations are given to confirm the theoretical analysis.
Cite this Article as
Chibueze Christian Okeke and Abdulmalik Usman Bello, Analysis of relaxed inertial method for non-convex mixed variational inequalities, Fixed Point Methods and Optimization, 1 (2024), 1–16