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IMA Journal of Mathematical Control and Information 2004 21(3):275-294; doi:10.1093/imamci/21.3.275
© 2004 by Institute of Mathematics and its Applications
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Strengthening Weierstrass’ condition

Javier F. Rosenblueth1 and Gerardo Sánchez Licea1

1 IIMAS–UNAM, Apartado Postal 20-726, México DF 01000, México

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.

Keywords: calculus of variations; sufficiency for local minima; Weierstrass and Legendre's strengthened conditions; singular extremals.

Received 4 June 2003.


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