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

* Correspondence: [email protected] College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China Full list of author information is available at the end of the article 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.