Differentiability of Convex Functions
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Fréchet 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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