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<title lang=en>Subdifferential characterization of quasiconvexity and convexity</title>
<creator>Aussel, Didier</creator>
<creator>Corvellec, Jean-Noël</creator>
<creator>Lassonde, Marc</creator>
<contributor>Procédés, Matériaux et Energie Solaire (PROMES) ; Université de Perpignan Via Domitia (UPVD) - Centre National de la Recherche Scientifique (CNRS)</contributor>
<contributor>LAboratoire de Mathématiques et PhySique (LAMPS) ; Université de Perpignan Via Domitia (UPVD)</contributor>
<contributor>Laboratoire de Mathématiques Informatique et Applications (LAMIA) ; Université des Antilles et de la Guyane (UAG)</contributor>
<description>International audience</description>
<source>Journal of Convex Analysis</source>
<publisher>Heldermann</publisher>
<identifier>hal-00699221</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00699221</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00699221</source>
<source>Journal of Convex Analysis, Heldermann, 1994, 1 (2), pp.195-201</source>
<language>en</language>
<subject>[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]</subject>
<type>info:eu-repo/semantics/article</type>
<type>Journal articles</type>
<description lang=en>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.</description>
<date>1994</date>
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