Generalized characterization of the convex envelope of a function

@article{Kadhi2002,
abstract = {We investigate the minima of functionals of the form\[\int \_\{[a,b]\}g(\dot\{u\}(s))\{\rm d\}s\]where $g$ is strictly convex. The admissible functions $u:[a,b]\rightarrow \mathbb \{R\}$ are not necessarily convex and satisfy $u\le f$ 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 $\bar\{f\}$, the convex envelope of $f$.},
author = {Kadhi, Fethi},
journal = {RAIRO - Operations Research - Recherche Opérationnelle},
keywords = {convex envelope; optimization; strict convexity; cost function; minima of functionals},
language = {eng},
number = {1},
pages = {95-100},
publisher = {EDP-Sciences},
title = {Generalized characterization of the convex envelope of a function},
url = {http://eudml.org/doc/245220},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Kadhi, Fethi
TI - Generalized characterization of the convex envelope of a function
JO - RAIRO - Operations Research - Recherche Opérationnelle
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 1
SP - 95
EP - 100
AB - We investigate the minima of functionals of the form\[\int _{[a,b]}g(\dot{u}(s)){\rm d}s\]where $g$ is strictly convex. The admissible functions $u:[a,b]\rightarrow \mathbb {R}$ are not necessarily convex and satisfy $u\le f$ 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 $\bar{f}$, the convex envelope of $f$.
LA - eng
KW - convex envelope; optimization; strict convexity; cost function; minima of functionals
UR - http://eudml.org/doc/245220
ER -