Second Order Directional Derivatives in Parametric Optimization Problems

We characterize the second order directional derivative in the sense of Ben-Tal and Zowe of a marginal function Ψ of the following general form: Ψ(x) − Inf{f(x, y) ∣ y ∈ Ω(x)}. This requires us to introduce some geometrical notions as, for example, the first and second order tangent directions to a multifunction. The main results are then applied to some particular types of marginal functions.