Strengthening Weierstrass' condition
Javier F. Rosenblueth · IMA Journal of Mathematical Control and Information · 2004
Sufficiency for strong local optimality in the calculus of variations involves, in the classical theory, the strengthened conditions of Legendre and Weierstrass. In particular, the former implies non‐singularity of the arc under consideration, an assumption which has been fundamental in any of the classical sufficiency theorems. Both conditions are removed and two sufficiency theorems, obtained by strengthening the classical necessary condition of Weierstrass in ways different than the usual one, are presented.