Journal ArticleDOI
On Sufficient Conditions in the Problems of Lagrange and Bolza
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This article is published in Annals of Mathematics.The article was published on 1936-07-01. It has received 11 citations till now.read more
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Book ChapterDOI
Normality and Abnormality in the Calculus of Variations
TL;DR: A number of papers concerning the problem of Bolza in the calculus of variations have been published which make it possible to carry through the theory of this problem with much simplified assumptions concerning what is called the normality of the minimizing arc as discussed by the authors.
Journal ArticleDOI
Entwicklungssätze aus der Theorie der zweiten Variation: Allgemeine Randbedingungen
Journal ArticleDOI
A direct sufficiency proof for the problem of Bolza in the calculus of variations
TL;DR: A sufficient proof for the problem of Bolza independent of assumptions of normality has been given by the author (IV) t and in a somewhat modified form by Bliss (VII) as mentioned in this paper.
A Direct Sufficiency Proof for a Weak Minimum in Optimal Control
TL;DR: In this paper, the authors derived a sufficiency theorem for a weak minimum of a fixed-endpoint optimal control problem, which is a generalization of the one introduced by Hestenes, in terms of directional convergent sequences of trajectories.
Journal ArticleDOI
The problem of Bolza in the calculus of variations
TL;DR: In this article, a set of differential equations Mx, y,y') satisfy a given set of equations and have their end values lying on a surface S in (x^yWy2)space.
References
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Journal ArticleDOI
Sufficient Conditions in the Problem of Lagrange with Fixed End Points
Journal ArticleDOI
Sufficient conditions in the problem of Lagrange without assumptions of normalcy
TL;DR: In this paper, it was shown that there is no condition of normalcy for an extremal to give a minimum in the Lagrange problem without assuming normalcy or analyticity.