New Gap Function And Its Successive Quadratic Programming Algorithm For General Mixed Variational Inequality Problems

The variational inequality problem is an important direction in nonlinear analysis.This thesis studies the gap function of the general mixed variational inequality problem on the basis of the predecessors,gives the regular gap function of the gap function,and analyzes the gap function.Continuity and differentiability studies,based on which we have given the corresponding algorithm research.We show our research content in the form of three chapters,as follows:In Chapterl,we introduce the concepts of general mixed variational inequal-ities and gap functions,and the background ancd significance of this dissertation.In chapter 2,wc propose a new gap fuinction for general mixed variational inequalities,and then use this new gap function to transform the general mixed variational inequality problem into a quadratic programming problem with linear approximation constraints.In chapter 3,we discuss the continuity and differentiability of the new gap function,and prove that the target variational inequality and the quadratic pro－gramming problem with linear approximation constraints have the same solution.In Chapter 4,we use the new gap function we defined,and give the contin-uous quadratic programming algorithm of general mixed variational inequality and the global convergence of this algorithm.