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In this paper we study, for certain problems in the calculus of variations and optimal control, two different questions related to uniqueness of multipliers appearing in first order necessary conditions. One deals with conditions under which a given multiplier associated with an extremal of a fixed function is unique, a property which, in nonlinear programming, is known to be equivalent to the strict Mangasarian-Fromovitz constraint qualifiocation. We show that, for isoperimetric problems in the calculus of variations, a similar characterization holds, but not in optimal control where the corresponding condition is only sufficient for the uniqueness of the multiplier. The other question is related to the set of multipliers associated with all functions for which a solution to the constrained problem is given. We prove that, for both types of problems, this set is a singleton if and only if a strong normality assumption holds. [ABSTRACT FROM AUTHOR]

The focus of this paper is on first order necessary conditions for optimal control problems with mixed state-control equality and inequality constraints. We consider the case when the cost and dynamics are nonsmooth, and the constraints satisfy Mangasarian-Fromowitz-type assumptions that weaken the commonly used hypothesis that the Jacobian of the active constraints, with respect to the free variable, is of full rank. The results are formulated as unmaximized Hamiltonian inclusion-type conditions involving not the customary product of partial subdifferentials but the joint subdifferential with respect to the state and control variables. [ABSTRACT FROM AUTHOR]

The focus of this paper is on first order necessary conditions for optimal control problems with mixed state-control equality and inequality constraints. We consider the case when the cost and dynamics are nonsmooth, and the constraints satisfy Mangasarian-Fromowitz-type assumptions that weaken the commonly used hypothesis that the Jacobian of the active constraints, with respect to the free variable, is of full rank. The results are formulated as unmaximized Hamiltonian inclusion-type conditions involving not the customary product of partial subdifferentials but the joint subdifferential with respect to the state and control variables. [ABSTRACT FROM AUTHOR]