Second-Order Derivatives of Extremal-Value Functions and Optimality Conditions for Semi-Infinite Programs

Second-order differential properties of an extremal-value function v are studied. It is shown that under certain assumptions (in particular the strong second-order sufficiency conditions) v is locally expressible as the maximum of a finite number of C²-functions. After removing the assumption of strong sufficiency lower and upper bounds on the second order local behaviour of v are proposed. The obtained results are applied to give second-order optimally conditions for a semi-infinite program.