Self-Adaptive Predictor-Corrector Approach for General Variational Inequalities Using a Fixed-Point Formulation. (12th March 2022) - Sanaullah, Kubra; Ullah, Saleem; Arif, Muhammad Shoaib; Abodayeh, Kamaleldin; Fayyaz, Rabia
Abstract : A literature review revealed that the general variational inequalities, fixed-point problems, and Winner–Hopf equations are equivalent. In this study, general variational inequality and fixed-point problem are considered. We introduced a new iterative method based on a self-adaptive predictor-corrector approach for finding a solution to the GVI. Adaptations in the fixed-point formulation and self-adaptive techniques have been used to predict a novel iterative approach. Convergence analyses of the suggested algorithm are demonstrated. Moreover, numerical analysis shows that we establish the new best method for solving general variational inequality which performs better than the previous one. Furthermore, it is known that GVI consisted of several classes including variational inequalities and related optimization problems, and results obtained in this study continue to hold for these problems.