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## Finitely determined functions and convex optimization

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Mohammed Bachir
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#### 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.

#### Domains

Mathematics [math] Functional Analysis [math.FA]

### Dates and versions

hal-01713851 , version 1 (21-02-2018)

### Identifiers

• HAL Id : hal-01713851 , version 2

### Cite

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

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