A practicable way for computing the directional derivative of the optimal value function in convex programming

Formulas for computing the directional derivative of the optimal value function or of lower or upper bounds of it are well-known from literature. Because they have as a rule a minimax structure, methods from nondifferentiable optimization are required. Considering a fully parameterized convex problem, in the paper the mentioned minimax formulas are transformed into usual programming problems. Although they are nonconvex in general, the computational effort is much lower than that for minimax problems. In several special cases, for instance, for linear least squares problems, linear programming problems arise.