Characterization of lower semicontinuous convex functions

Characterization of lower semicontinuous convex functions
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by R. Correa, A. Jofré and L. Thibault PDF

Proc. Amer. Math. Soc. 116 (1992), 67-72 Request permission

We prove that a lower semicontinuous function defined on a reflexive Banach space is convex if and only if its Clarke subdifferential is monotone.

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