# Finitely determined functions and convex optimization

1 Equations d'evolution
SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
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.
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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, January 19, 2021 - 11:09:04 AM
Long-term archiving on: : Friday, May 31, 2019 - 1:53:42 PM

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• HAL Id : hal-01713851, version 2

### Citation

Mohammed Bachir, Adrien Fabre, Sebastian Tapia-Garcia. Finitely determined functions and convex optimization. 2019. ⟨hal-01713851v2⟩

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