| Issue |
RAIRO-Oper. Res.
Volume 36, Number 1, January-March 2002
|
|
|---|---|---|
| Page(s) | 95 - 100 | |
| DOI | https://doi.org/10.1051/ro:2002007 | |
| Published online | 15 July 2002 | |
Generalized Characterization of the Convex Envelope of a Function
Preparatory Institute of Engineering Studies,
P.O. Box 805, 3018 Sfax, Tunisia.
Received:
June
2001
We investigate the minima of functionals of the form ![$$\int_{[a,b]}g(\dot u(s)){\rm d}s$$](/articles/ro/abs/2002/01/ro2203/ro2203_tex_eq1.png)
where g is strictly convex. The admissible functions ![$u:[a,b]\longrightarrow\mathbb{R}$](/articles/ro/abs/2002/01/ro2203/ro2203_tex_eq2.png)
are not necessarily
convex and satisfy 
on [a,b], u(a)=f(a), u(b)=f(b), f is a fixed function on [a,b].
We show that the minimum is attained by 
, the convex envelope of f.
Key words: Convex envelope / optimization / strict convexity / cost function.
© EDP Sciences, 2002
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.