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 
of a lineat space 
supplied with a norm which assigns a “length” to each y Є 
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© 1983 Springer-Verlag New York Inc.
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Troutman, J.L. (1983). Local Extrema in Normed Linear Spaces. In: Variational Calculus with Elementary Convexity. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0158-5_6
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DOI: https://doi.org/10.1007/978-1-4684-0158-5_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0160-8
Online ISBN: 978-1-4684-0158-5
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