Directional derivative of a class of set-valued mappings and its application

Calculating the directional derivative of a class of the set-valued mappings G(x) = {z \ Az less than or equal to h(x)}, in the sense of Tyurin (1965) and Banks & Jacobs (1970) is presented that can be viewed as an extension to the one given by Pecherskaya. Results obtained in this paper are used to get a bound of the Lipschitz constant for the solution sets of the perturbed Linear Programming. This new bound is smaller than the one, due to Li (1994).