On the Boundedness and Stability of Solutions to the Affine Variational Inequality Problem

Abstract

This paper investigates the boundedness and stability of solutions to the affine variational inequality problem. The concept of a solution ray to a variational inequality defined by an affine, mapping and on a closed convex set is introduced and characterized; the connection of such a ray with the boundedness of the solution set of the given problem is explained. In the case of the monotone affine variational inequality, a complete description of the solution set is obtained which leads to a simplified characterization of the boundedness of this set as well as to a new error bound result for approximate solutions to such a variational problem. The boundedness results are then combined with certain degree- theoretic arguments to establish the stability of the solution set of an affine variational inequality problem.