On the Subdifferentiability of Convex Functions
نویسنده
چکیده
(Thus the subgradients of / correspond to the nonvertical supporting hyperplanes to the convex set consisting of all the points of E®R lying above the graph of /.) The set of subgradients of / at x is denoted by dfix). If d/(x) is not empty, / is said to be subdifferentiable at x. If/actually had a gradient x* = V/(x) at x in the sense of Gateaux (or Frechet), one would in particular have d/(x) = {V/(x)} (see Moreau [5, p. 20]). It is immediate from (1.2) that dfix) is a weak* closed convex set in E* for each xGP, and that the effective domain
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