Research On Two Kinds Of Vector Variationalinequalities Based On Image Space Analysis

This thesis focuses on two kinds of vector variational inequalities,namely the constrained vector variational inequality and the constrained inverse vector variational inequality.Both of them are important generalized forms of variational inequalities and can be converted to each other under certain conditions.By using the tool of image space analysis,the oriented distance function and the corresponding norm are introduced to construct a nonlinear regular weak separation function.Then a gap function of the constrained vector variational inequality is obtained by using the nonlinear regular weak separation function and its corresponding properties are studied.Finally,the error bound result of the solution is obtained under some mild assumptions.For the constrained inverse vector variational inequality,it is a very important generalization form of the classical vector variational inequality and has a wider application.Therefore,it is necessary to study its further properties with the help of image space analysis.Firstly,the regular weak separation function under different parameter sets is constructed by nonlinear separation method and its properties are studied.Then we establish the alternative theorem under certain conditions and obtain the necessary and sufficient optimality conditions for the solutions of constrained inverse vector variational inequalities.At last,two different gap functions are obtained under the constrained inverse vector variational inequality problem,and the error bound result is obtained under the assumption that the solution set is generalized monotone.These error bounds provide an effective distance estimation between exact solutions and feasible points of two kinds of vector variational inequalities,respectively.