Second-order sufficiency criteria and local convexity for equivalent problems in the calculus of variations
type: Item
instance of: scholarly article
title: Second-order sufficiency criteria and local convexity for equivalent problems in the calculus of variations
zbMATH Open document ID: 0698.49019
DOI: 10.1016/0022-247X(90)90321-6
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: Two classical theorems regarding sufficient conditions for optimality in the calculus of variations receive new proofs in this paper. The author shows that if the strengthened forms of the classical Euler-Lagrange, Weierstrass, Legendre, and Jacobi conditions hold along a certain arc x(t), then one can construct a variational problem equivalent to the original one which is locally convex near x(t). The classical sufficiency theorems follow from this, because in convex problems the first-order necessary conditions are also sufficient.
Mathematics Subject Classification ID: 49L99
zbMATH DE Number: 4144821
zbMATH Keywords: sufficient conditions for optimality
zbMATH Keywords: Euler-Lagrange, Weierstrass, Legendre, and Jacobi conditions
zbMATH Keywords: convex problems
author: P. D. Loewen
reviewed by: P. D. Loewen
MaRDI profile type: Publication
cites work: Sufficiency and the Jacobi Condition in the Calculus of Variations
cites work: Sufficient Conditions in the Calculus of Variations and in the Theory of Optimal Control
cites work: Conjugate convex functions in optimal control and the calculus of variations
cites work: Q3673540
cites work: Sufficient Conditions for the Generalized Problem of Bolza
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description: scientific article; zbMATH DE number 4144821