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A GENERAL STATEMENT OF DUAL FIRST-ORDER SUFFICIENT OPTIMALITY CONDITIONS FOR THE GENERALIZED PROBLEM OF BOLZA

In this paper we provide first-order sufficient optimality conditions for the generalized problem of Bolza when all arcs take values in a separable Hilbert space. Our approach consists in the explicit construction of a quadratic function that satisfies the dual Hamilton-Jacobi inequality. The essential role in the generalized conditions plays the existence of a certain function for which a certain inequality holds.