Existence and duality theorems for convex problems of Bolza

Abstract

The theory of conjugate convex functions is applied to a fundamental class of “convex” problems in the calculus of variations and optimal control. This class has many special properties which have not previously been exploited and for which the standard methods of approach are inadequate. Duality theorems are established which yield new results on the existence of optimal arcs, as well as necessary and sufficient conditions for optimality. These results have some relevance also to the study of “nonconvex” problems.