Ms. Gowda et Js. Pang, ON THE BOUNDEDNESS AND STABILITY OF SOLUTIONS TO THE AFFINE VARIATIONAL INEQUALITY PROBLEM, SIAM journal on control and optimization, 32(2), 1994, pp. 421-441
This paper investigates the boundedness and stability of solutions to
the affine variational inequality problem. The concept of a solution r
ay to a variational inequality defined by an affine mapping and on a c
losed convex set is introduced and characterized; the connection of su
ch a ray with the boundedness of the solution set of the given problem
is explained. In the case of the monotone affine variational inequali
ty, a complete description of the solution set is obtained which leads
to a simplified characterization of the boundedness of this set as we
ll as to a new error bound result for approximate solutions to such a
variational problem. The boundedness results are then combined with ce
rtain degree-theoretic arguments to establish the stability of the sol
ution set of an affine variational inequality problem.