Error Bounds For Affine Variational Inequalities With Semi-Definite-Cone Constraints

This paper mainly studies the Lipschitz error bound of the semi-definite-cone affine variational inequality problem.In the conclusions of the existing variational inequality error bounds,it is necessary to have strong monotonic conditions in the inequality,or the constraint to be a set of special structures such as polyhedrons and second-order cones.In my paper,we will study the sufficient conditions for Lipschitz error bound of the affine variational inequality with linear semiconstricted cone constraints.Firstly,the problem is transformed into the equivalent projection fixed-point form,and its projection point is the solution of a quadratic objective semi-definite programming.In this paper,according to the error bound property of the KKT system of a semi-definite programming problem,also the error bound conclusions for Lipschitz functions,we investigate sufficient conditions for Lipschitz error bound to hold for the considered problem.Under some reasonable assumptions,it is proved that the Robinson constraint qualification is a sufficient condition for local Lipschitz error bound to be valid for affine variational inequalities with linear semi-confined cone constraints.