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Finitely determined functions and convex optimization
Abstract : We study the notion of {\it finitely determined functions} defined on a topological vector space $E$ equipped with a biorthogonal system. This notion will be used to obtain a necessary and sufficient condition for a convex function to attain a minimum at some point. An application to the Karush-Kuhn-Tucker theorem will be given. For real-valued convex functions defined on a Banach space with a Schauder basis, the notion of finitely determined function coincides with the classical continuity but outside the convex case there are many finitely determined nowhere continuous functions.
Cited literature [19 references]
https://hal-paris1.archives-ouvertes.fr/hal-01713851
Contributor : Mohammed Bachir <>
Submitted on : Saturday, March 2, 2019 - 7:19:42 PM
Last modification on : Tuesday, July 21, 2020 - 3:39:59 AM
Document(s) archivé(s) le : Friday, May 31, 2019 - 1:53:42 PM
Contributor : Mohammed Bachir <>
Submitted on : Saturday, March 2, 2019 - 7:19:42 PM
Last modification on : Tuesday, July 21, 2020 - 3:39:59 AM
Document(s) archivé(s) le : Friday, May 31, 2019 - 1:53:42 PM
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