Journal Article

Strengthening Weierstrass’ condition

Javier F. Rosenblueth and Gerardo Sánchez Licea

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 21, issue 3, pages 275-294
Published in print September 2004 | ISSN: 0265-0754
Published online September 2004 | e-ISSN: 1471-6887 | DOI:
Strengthening Weierstrass’ condition

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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

Journal Article.  0 words. 

Subjects: Mathematics

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