Geodesic
There are Many Totally Convex Functions
Journal of convex analysis, Tome 13 (2006) no. 3, pp. 623-632

Voir la notice de l'article provenant de la source Heldermann Verlag

Let $K$ be a convex subset of a normed linear space and let $R^1$ denote the real line. We show that there are many (in the sense of Baire category) strictly convex and totally convex functions $f \colon K \to R^1$. It is known that the existence of such functions is crucial in numerous optimization algorithms.
Classification : 46N10, 52A41, 54E50, 54E52
Mots-clés : Complete metric space, essentially strictly convex function, generic property, strictly convex function, totally convex function 
@article{JCA_2006_13_3_JCA_2006_13_3_a8,
     author = {D. Butnariu and S. Reich and A. J. Zaslavski},
     title = {There are {Many} {Totally} {Convex} {Functions}},
     journal = {Journal of convex analysis},
     pages = {623--632},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2006},
     url = {http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a8/}
}
TY  - JOUR
AU  - D. Butnariu
AU  - S. Reich
AU  - A. J. Zaslavski
TI  - There are Many Totally Convex Functions
JO  - Journal of convex analysis
PY  - 2006
SP  - 623
EP  - 632
VL  - 13
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a8/
ID  - JCA_2006_13_3_JCA_2006_13_3_a8
ER  - 
%0 Journal Article
%A D. Butnariu
%A S. Reich
%A A. J. Zaslavski
%T There are Many Totally Convex Functions
%J Journal of convex analysis
%D 2006
%P 623-632
%V 13
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a8/
%F JCA_2006_13_3_JCA_2006_13_3_a8
D. Butnariu; S. Reich; A. J. Zaslavski. There are Many Totally Convex Functions. Journal of convex analysis, Tome 13 (2006) no. 3, pp. 623-632. http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a8/