Sufficiency and Augmentability for the Problem of Lagrange

摘要

In this paper we introduce the notions of weak and strong augmentability for the problem of Lagrange in the calculus of variations involving equality constraints. In particular, we show that the standard sufficient conditions for a strong minimum imply strong augmentability which in turn implies local optimality. This is a crucial aspect of the theory since it provides an alternative approach not only to the derivation of necessary conditions but also for sufficiency results.