Abstract

Let f : X → ℝ ∪ {+∞} be a lower semicontinuous function on a Banach space X. We show that f is quasiconvex if and only if its Clarke subdifferential ∂f is quasimonotone. As an immediate consequence, we get that f is convex if and only if ∂f is monotone.

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Didier Aussel

Mathématiques Appliquées, Université Blaise Pascal, Clermont-Ferrand, F-63177 Aubière Cedex, France.

Jean-Noël Corvellec

Mathématiques, Université de Perpignan, F-66860 Perpignan Cedex, France.

Marc Lassonde

Mathématiques, Université des Antilles et de la Guyane, F-97159 Pointe-à-Pitre Cedex, Guadeloupe, France.

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Suggested citation

D. Aussel, J.-N. Corvellec, M. Lassonde. “Subdifferential Characterization of Quasiconvexity and Convexity.” Journal of Convex Analysis 1 (1994), No. 2, 195–201. https://doi.org/10.68381/jca01014

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Published by Heldermann Verlag, 1994. Rights now held by Banach Press LLC.