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.
Author information
Contact details are reproduced from the original publication and may be historical.
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.
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
Published by Heldermann Verlag, 1994. Rights now held by Banach Press.
Didier Aussel
