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Conjugacy in Convex Analysis

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Fundamentals of Convex Analysis

Part of the book series: Grundlehren Text Editions ((TEXTEDITIONS))


In classical real analysis, the gradient of a differentiable function f : ℝn → ℝ. plays a key role - to say the least. Considering this gradient as a mapping xs(x) = ∇f(x) from (some subset X of) ℝn to (some subset S of) ℝn, an interesting object is then its inverse: to a given sS, associate the xX such that s =f(x). This question may be meaningless: not all mappings are invertible! but could for example be considered locally, taking for X x S a neighborhood of some (x 0, s 0 = ∇f(x 0)), with ∇2 f continuous and invertible at x 0 (use the local inverse theorem).

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© 2001 Springer-Verlag Berlin Heidelberg

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Hiriart-Urruty, JB., Lemaréchal, C. (2001). Conjugacy in Convex Analysis. In: Fundamentals of Convex Analysis. Grundlehren Text Editions. Springer, Berlin, Heidelberg.

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42205-1

  • Online ISBN: 978-3-642-56468-0

  • eBook Packages: Springer Book Archive

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