Proximal Projection-Like Method For Generalized Mixed Variational Inequalities

This thesis mainly studies proximal projection-like method for generalized mixed variational inequalities.The first chapter introduces the background and significance of this paper.The second chapter describes the distancelike function and the projection-like maps.In the third chapter,we obtain intermediate iteration point by the proximal point method containing inexact solutions,and then by using the projection-like algorithm,we project the intermediate iteration point onto the feasible set of generalized mixed variational inequalities to get the next iteration point.We prove that the iterative sequence converges to the solution of generalized mixed variational inequalities when set-valued mapping is pseudo-monotone.