Abstract
Fr9chet differentiability, Gâteaux differentiability, directional differentiability, subdifferentiability, and continuity are notions that are closely related to each other. In this chapter, we provide fundamental results on these relationships, as well as basic results on the steepest descent direction, the Chebyshev center, and the max formula that relates the directional derivative to the support function of the subdifferential at a given point.
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© 2011 Springer Science+Business Media, LLC
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Bauschke, H.H., Combettes, P.L. (2011). Differentiability of Convex Functions. In: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9467-7_17
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DOI: https://doi.org/10.1007/978-1-4419-9467-7_17
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-9466-0
Online ISBN: 978-1-4419-9467-7
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