The Existence And Iterative Algorithms Of Solutions For Some Variational Inequalities

This graduation thesis introduced and studied the existence and iterative algorithms of solutions for some nonconvex set-valued variational inequalities, nonconvex setvalued quasi-variational inequalities and convex single-valued quasi-variational inequalities.This article is composed by five partsIn chapter 1, the background of the topic has been introduced. The main research questions, architecture also have been summarized. In chapter 2, some useful knowledge has been listed.In chapter 3, the existence and iterative algorithms of solutions for nonconvex set-valued variational inequalities have been discussed. It is well known that the equivalence between nonconvex set-valued variational inequalities and fixed point problems as well as the nonconvex set-valued variational inclusions has been established. Then using this equivalent equations, we discuss the existence of solutions for the nonconvex set-valued variational inequalities, under the condition of the set-valued map is relaxed-monotone and?H- Lipschitz. And using this equivalence among the three to construct iterative algorithms for finding the solutions of this nonconvex set-valued variational inequalities, we also discuss the convergence of the iterative method under the condition that the set-valued map is relaxed-monotone and?H- Lipschitz.In chapter 4, the existence and iterative algorithms of solutions for nonconvex set-valued quasi-variational inequalities have been discussed. The equivalence among nonconvex setvalued quasi-variational inequalities, nonconvex set-valued quasi-variational inclusions and fixed point problems has been established. The existence of solutions for the nonconvex setvalued quasi-variational inequalities has been discussed by using the equivalence, on the condition that the set-valued map is relaxed-monotone and?H- Lipschitz. Applying this equivalent formulation to construct iterative algorithms for finding the solutions of this nonconvex setvalued quasi-variational inequalities. We also give the convergence of the iterative method under the condition that the set-valued map is relaxed-monotone and?H- Lipschitz.In chapter 5, convex single-valued quasi-variational inequalities have been discussed. Using the projection on non-empty closed convex set, we construct iterative algorithms of solutions for convex single-valued quasi-variational inequalities. The feasibility and convergence of the iterative method also have been studied in the situation that the map is pseudo-monotone.