Abstract
We have mentioned in our preamble to Chap. C that sublinearity permits the approximation of convex functions to first order around a given point. In fact, we will show here that, if f : ℝn → ℝ is convex and x ∈ ℝn is fixed, then the function
exists and is finite sublinear. Furthermore, f′ approximates f around x in the sense that
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© 2001 Springer-Verlag Berlin Heidelberg
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Hiriart-Urruty, JB., Lemaréchal, C. (2001). Subdifferentials of Finite Convex Functions. In: Fundamentals of Convex Analysis. Grundlehren Text Editions. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56468-0_5
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DOI: https://doi.org/10.1007/978-3-642-56468-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42205-1
Online ISBN: 978-3-642-56468-0
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