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

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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 
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     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/}
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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/