Convergence analysis of projection methods for a new system of general nonconvex variational inequalities

Abstract

In this article, we introduce and consider a new system of general nonconvex variational inequalities defined on uniformly prox-regular sets. We establish the equivalence between the new system of general nonconvex variational inequalities and the fixed point problems to analyze an explicit projection method for solving this system. We also consider the convergence of the projection method under some suitable conditions. Results presented in this article improve and extend the previously known results for the variational inequalities and related optimization problems. MSC (2000): 47J20; 47N10; 49J30.

Further Investigation on the Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities withk-Strict Pseudocontractions

“…It has been shown that variational inequalities provide the most natural, direct, simple, and efficient framework for a general treatment of some unrelated problems arising in various fields of pure and applied sciences. In recent years, there have been considerable activities in the development of numerical techniques including projection methods, Wiener-Hopf equations, auxiliary principle, and descent framework for solving variational inequalities; see [2][3][4][5][6][7][8][9][10][11][12][13][14][15] and the references therein.…”