On Characterizing The Solution Sets Of A Class Of Generalized Variational Inequalities Problems

In recent years, variational inequality theory has become the very popular fieldin nonlinear analysis. Under the appropriate assumptions, the solution set ofvariational inequality problems is consistent with the optimal solution set of theoptimization problem. Therefore, to explore and study the variational inequalityproblem has become an important part of nonlinear analysis. So as to meet thedemands of solving practical problems, many generalizations to variationalinequality have been made, among which variational inequalities under the lowerDini derivative condition is an important form. Therefore, it is significant to studythe relationship between this kind of generalized variational inequalities andoptimization problem. The purpose of this paper is to study the nature of solutionset of variational inequalities under the lower Dini derivative condition, and discussthe relationship between this kind of generalized variational inequalities andoptimization problem. In addition, to study the relationship between vectorvariational inequalities under the lower Dini derivative condition and the radialregressive of vector function, as well as the solution sets of vector optimizationproblems.The outline of the thesis is as follows.In chapter1, we introduce the current situation of variational inequalityproblems.In chapter2, we present some preliminaries for the full article.In chapter3, we focus on the nature of solution set of the generalizedvariational inequalities. we construct a class of gap functions of the generalizedMinty variational inequalities using the lower Dini derivative, and give a simplecharacterization of both solution sets of the generalized Stampacchia variationalinequality problem and the generalized Minty variational inequality problem.In chapter4, we focus on the relationship between the solution set of thegeneralized variational inequalities and optimal solution set of optimization problem.In chapter5, we mainly discussed the relationship between vector variational inequalities under the lower Dini derivative condition and the radial regressive ofvector function, as well as the solution sets of vector optimization problems.In chapter6, we give a summary of this paper and put forward some problemsfor further study.