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<datestamp>2018-01-11</datestamp>
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<publisher>HAL CCSD</publisher>
<title lang=en>Nonsmooth constrained optimization and multidirectional mean value inequalities</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>ISSN: 1052-6234</source>
<source>SIAM Journal on Optimization</source>
<publisher>Society for Industrial and Applied Mathematics</publisher>
<identifier>hal-00699204</identifier>
<identifier>https://hal.archives-ouvertes.fr/hal-00699204</identifier>
<source>https://hal.archives-ouvertes.fr/hal-00699204</source>
<source>SIAM Journal on Optimization, Society for Industrial and Applied Mathematics, 1999, 9 (3), pp.690-706</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>We establish a general Fermat rule for the problem of minimizing a lower semicontinuous function on a convex subset of a Banach space. Our basic tool is a constrained variational principle derived from the "smooth" variational principle of Borwein and Preiss. Specializing the Fermat rule to the case when the convex set is a "drop," we obtain a multidirectional Rolle-type inequality from which, in turn, we deduce a multidirectional mean value inequality, in the line of Clarke and Ledyaev. We follow the abstract approach of our previous paper [Trans. Amer. Math. Soc., 347 (1995), pp. 4147-4161], thus covering all standard situations met in applications, while stressing the links between the results and the few key properties that are needed.</description>
<date>1999</date>
</dc>
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