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.
Complete list of metadatas

Cited literature [19 references]  Display  Hide  Download

https://hal-paris1.archives-ouvertes.fr/hal-01713851
Contributor : Mohammed Bachir <>
Submitted on : Saturday, March 2, 2019 - 7:19:42 PM
Last modification on : Monday, May 11, 2020 - 4:20:51 PM
Document(s) archivé(s) le : Friday, May 31, 2019 - 1:53:42 PM

Files

Finitely_det_02_03_2019.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01713851, version 2

Collections

Citation

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

Share

Metrics

Record views

93

Files downloads

215