ON THE LIPSCHITZIAN PROPERTIES OF POLYHEDRAL MULTIFUNCTIONS

In this paper, we show that for a polyhedral multifunction F: R(n) --> R(m) with convex range, the inverse function F-1 is locally lower Lip schitzian at every point of the range of F (equivalently Lipschitzian on the range of Fl if and only if the function F is open. As a consequ ence, we show that for a piecewise affine function f: R(n) --> R(n), f is surjective and f(-1) is Lipschitzian if and only if f is coherentl y oriented. An application, via Robinson's normal map formulation, lea ds to the following result in the context of affine variational inequa lities: the solution mapping (as a function of the data vector) is non empty-valued and Lipschitzian on the entire space if and only if the s olution mapping is single-valued, This extends a recent result of Murt hy, Parthasarathy and Sabatini, proved in the setting of linear comple mentarity problems.