Abstract
In ℝd, it is possible to give conditions which are necessary in order that a function f have a local extremal value on a subset D, expressed in terms of the vanishing of its gradient ∇f (§0.5). In this chapter, we shall obtain analogous variational conditions which are necessary to characterize local extremal values of a function J on a subset D of a linear space Y supplied with a norm which assigns a “length” to each y ∈ Y.
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© 1996 Springer Science+Business Media New York
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Troutman, J.L. (1996). Local Extrema in Normed Linear Spaces. In: Variational Calculus and Optimal Control. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0737-5_6
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DOI: https://doi.org/10.1007/978-1-4612-0737-5_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6887-1
Online ISBN: 978-1-4612-0737-5
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