A Strict Mangasarian-Fromovitz Type Condition for Isoperimetric Control Problems

The aim of this paper is to improve a well-known result on second order necessary conditions for optimal control problems involving inequality and equality isoperimetric constraints. The improvement, which widens its range of applicability, consists in weakening the classical assumption under which a certain quadratic form is nonnegative along a cone of critical directions. The new, weaker assumption is shown to be equivalent to a strict Mangasarian-Fromovitz type condition which, in turn, implies regularity relative to the contingent cone of a subset of the original set of constraints. An example is given which lies beyond the scope of previous approaches and illustrates the usefulness of our main result.