On the Lipschitzian properties of polyhedral multifunctions. (English) Zbl 0854.49010
Summary: In this paper, we show that for a polyhedral multifunction with convex range, the inverse function is locally lower Lipschitzian at every point of the range of (equivalently, Lipschitzian on the range of if and only if the function is open. As a consequence, we show that for a piecewise affine function , is surjective and is Lipschitzian if and only if is coherently oriented. An application, via Robinson’s normal map formulation, leads to the following result in the context of affine variational inequalities: the solution mapping (as a function of the data vector) is nonempty-valued and Lipschitzian on the entire space if and only if the solution mapping is single-valued. This extends a recent results of Murthy, Parthasarathy and Sabatini, proved in the setting of linear complementarity problems.
|49J40||Variational methods including variational inequalities|
|90C33||Complementarity and equilibrium problems; variational inequalities (finite dimensions)|