Three novel inertial subgradient extragradient methods for quasi-monotone variational inequalities in Banach spaces

In this paper, we introduce three new inertial subgradient extragradient methods for solving variational inequalities involving quasi-monotone operators in the setting of 2-uniformly convex and uniformly smooth Banach spaces. We dispense with the well-known requirement of the stepsizes of the subgradient extragradient method on the prior knowledge of the Lipschitz constant of the cost function in our proposed algorithms. Furthermore, we give many numerical examples to test the robustness of our proposed algorithms and compare their performance with several algorithms in the literature. In addition, we use our proposed algorithms in the restoration process of some degraded images and compare the quality of the restored images using our proposed algorithms and some recent algorithms in the literature. Finally, from the results of the numerical simulations, our proposed algorithms are competitive and promising.