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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- © Copyright 1983 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 275 (1983), 561-586
- MSC: Primary 49C05
- DOI: https://doi.org/10.1090/S0002-9947-1983-0682718-3
- MathSciNet review: 682718