ON THE CONTINUITY OF THE SOLUTION MAP IN LINEAR COMPLEMENTARITY PROBLEMS

The continuity properties of the solution map y :(M, q) -> (M, q) are investigated, where y(M, q) denotes the solution set corresponding to the linear complementarity problem LCP(M, q). A Robinson-type upper semicontinuity result is established for y, and a generalization of the Mangasarian-Shiau result concerning the Lipschitzian property of y in the q-variable is proved. It is also shown that when the matrix is positive semidefinite (or more generally a G-matrix), the solution map is Lipschitz continuous with respect to the q-vector if and only if the matrix is a P-matrix.