Abstract
We shall state, here, some theorems that characterize solutions to the problem of Bolza in the calculus of variations. The proofs of some of these theorems will only be briefly outlined. The reader may refer to Bliss [8] and [9] and to Pars [40] for a more detailed presentation. By way of introduction we discuss an unconstrained problem in the calculus variation, in section 1. In section 2, we state the problem of Bolza. In section 3 we discuss first order necessary conditions and in section 4 we state the necessary conditions of Weierstrass, Clebsch, and Mayer. In section 5, we state second order sufficient conditions. In section 6, we characterize solutions to problem A′.
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© 1971 Springer-Verlag Berlin · Heidelberg
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El-Hodiri, M.A. (1971). The Problem of Bolza with Equality Constraints. In: Constrained Extrema Introduction to the Differentiable Case with Economic Applications. Lecture Notes in Operations Research and Mathematical Systems, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80657-5_6
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DOI: https://doi.org/10.1007/978-3-642-80657-5_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-05637-9
Online ISBN: 978-3-642-80657-5
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