Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [19 references]  Display  Hide  Download
Contributor : Mohammed Bachir Connect in order to contact the contributor
Submitted on : Saturday, March 2, 2019 - 7:19:42 PM
Last modification on : Wednesday, November 17, 2021 - 12:33:35 PM
Long-term archiving on: : Friday, May 31, 2019 - 1:53:42 PM


 Restricted access
To satisfy the distribution rights of the publisher, the document is embargoed until : 2023-05-12

Please log in to resquest access to the document


  • HAL Id : hal-01713851, version 2



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



Les métriques sont temporairement indisponibles