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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Sufficient conditions for the generalized problem of Bolza

Author: Vera Zeidan
Journal: Trans. Amer. Math. Soc. 275 (1983), 561-586
MSC: Primary 49C05
MathSciNet review: 682718
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Abstract: This paper presents sufficient conditions for strong local optimality in the generalized problem of Bolza. These conditions represent a unification, in the sense that they can be applied to both the calculus of variations and to optimal control problems, as well as problems with nonsmooth data. Also, this paper brings to light a new point of view concerning the Jacobi condition in the classical calculus of variations, showing that it can be considered as a condition which guarantees the existence of a canonical transformation which transforms the original Hamiltonian to a locally concave-convex Hamiltonian.

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Keywords: Sufficient conditions, strong local minimality, generalized problem of Bolza, canonical transformations, calculus of variations, conjugate points, Jacobi condition
Article copyright: © Copyright 1983 American Mathematical Society