Hybrid Iterative Scheme for Variational Inequality Problem Involving Pseudo-monotone Operator with Application in Signal Recovery

In this article, we propose a hybrid iterative scheme with strong convergence property for solving variational inequality problems. The algorithm uses a self-adaptive stepsize defined using a simple updating rule. Therefore, the method does not require prior knowledge of the Lipschitz constant of the underlying operator. We consider a more general set of operators as the underlying operators. Moreover, we derived a fixed stepsize scheme from the proposed method. Under some suitable conditions, we show the strong convergence of the iterates generated by the proposed and the derived algorithms. Furthermore, we present numerical experiments to illustrate the computational performance of the proposed algorithm in comparison with some of the existing algorithms in the literature. Additionally, as an application, we use the proposed algorithm to solve the problem of recovering an original signal from a noisy signal.