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A practicable way for computing the directional derivative of the optimal value function in convex programming
Abstract: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 minmax structure, methods from nondifferentiable optimization are required.

Considering a fully parametrized convex problem, in the paper the mentioned minmax formulas are transformed into usual programming problems. Although they are nonconvex in general, the computational effort is much lower than that for minmax problems. In several special cases, for instance, for linear least squares problems, linear programming problems arise.
Keywords:Directional Derivative  Optimal Value Function  Convex Programming  Parametric Optimization  Least Squares  Quadratic Programming  Linear Programming  Sensitivity Analysis
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