Solving Equilibrium Problem with New Inertial Technique
Chidi Elijah Nwakpa, Chinedu Izuchukwu, Chibueze CHristian Okeke, Dilber Uzun Ozsahin, Abubakar Adamu
TL;DR
The paper addresses solving equilibrium problems EP in real Hilbert spaces when the bifunction f is pseudomonotone and satisfies Lipschitz-type conditions. It proposes a subgradient extragradient method augmented with one inertial term and two correction terms, plus a self-adaptive stepsize, to accelerate convergence. Under standard assumptions, the method achieves weak convergence to a solution of EP, and when f is β-strongly pseudomonotone, it attains an R-linear convergence rate to the unique solution. Numerical experiments show the approach outperforms several existing methods across multiple test problems, highlighting practical gains in convergence speed and efficiency for large-scale EPs.
Abstract
We propose in this work a subgradient extragradient method with inertial and correction terms for solving equilibrium problems in a real Hilbert space. We obtain that the sequence generated by our proposed method converges weakly to a point in the solutions set of the equilibrium problem when the associated bivariate function is pseudomonotone and satisfies Lipschitz conditions. Furthermore, in a case where the bifunction is strongly pseudomonotone, we establish a linear convergence rate. Lastly, through different numerical examples, we demonstrate that the incorporation of multiple correction terms significantly improves our proposed method when compared with other methods in the literature.