Abstract

In a well-known paper by Kyparisis it is proved that, in nonlinear programming, the uniqueness of Lagrange multipliers is equivalent to a strict version of the Mangasarian-Fromovitz constraint qualification which, in turn, implies the satisfaction of second-order necessary optimality conditions. This is no longer the case in optimal control where, as shown in a recent paper, the corresponding strict constraint qualification is only sufficient for the uniqueness of multipliers. In this paper we exhibit the missing piece: a new, simple condition, implied by the strict constraint qualification, which is necessary and sufficient for the uniqueness of multipliers in optimal control.