Local Extrema in Normed Linear Spaces
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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