Geodesic
Comparing Fenchel-Moreau Conjugates with Level Set Conjugates
Journal of convex analysis, Tome 15 (2008) no. 2, pp. 285-297

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

We compare the Fenchel-Moreau second conjugates associated to an arbitrary coupling function $\varphi :X\times W\rightarrow \overline{R}=[-\infty ,+\infty ]$ between two sets $X$ and $W$ with the second level set conjugates associated to the same coupling. For a coupling $\varphi :R^{n}\times R^{n}\rightarrow R=(-\infty ,+\infty )$ that is additively homogeneous in one (or both) of the variables we also compare the first conjugates associated to the same coupling. We give an application to the ``min-type'' coupling function arising in the study of topical functions.
Classification : 49N15, 26B25, 52A01
Mots-clés : Generalized conjugation, topical functions, hull operators 
@article{JCA_2008_15_2_JCA_2008_15_2_a6,
     author = {J.-E. Mart{\'\i}nez-Legaz and I. Singer},
     title = {Comparing {Fenchel-Moreau} {Conjugates} with {Level} {Set} {Conjugates}},
     journal = {Journal of convex analysis},
     pages = {285--297},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JCA_2008_15_2_JCA_2008_15_2_a6/}
}
TY  - JOUR
AU  - J.-E. Martínez-Legaz
AU  - I. Singer
TI  - Comparing Fenchel-Moreau Conjugates with Level Set Conjugates
JO  - Journal of convex analysis
PY  - 2008
SP  - 285
EP  - 297
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JCA_2008_15_2_JCA_2008_15_2_a6/
ID  - JCA_2008_15_2_JCA_2008_15_2_a6
ER  - 
%0 Journal Article
%A J.-E. Martínez-Legaz
%A I. Singer
%T Comparing Fenchel-Moreau Conjugates with Level Set Conjugates
%J Journal of convex analysis
%D 2008
%P 285-297
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JCA_2008_15_2_JCA_2008_15_2_a6/
%F JCA_2008_15_2_JCA_2008_15_2_a6
J.-E. Martínez-Legaz; I. Singer. Comparing Fenchel-Moreau Conjugates with Level Set Conjugates. Journal of convex analysis, Tome 15 (2008) no. 2, pp. 285-297. http://geodesic.mathdoc.fr/item/JCA_2008_15_2_JCA_2008_15_2_a6/