Directional derivatives of optimal value functions in mathematical programming (Q1333364)

This paper contains sufficient conditions for the existence of a (one-sided) directional derivative \(F'(x,d)\) where \(F(x) = \inf \{f(x,y) |y \in S\}\) is an optimal value function for a parametric nonlinear programming problem in finite dimensional spaces. Contrary to almost all the results known so far, it is not assumed here that the active set at \(x\) given by \(N^* (x) = \{y \in S |f(x,y) = F(x)\}\) is nonempty.