Geodesic
Convex Coradiant Sets with a Continuous Concave Cogauge
Journal of convex analysis, Tome 15 (2008) no. 2, pp. 325-343

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

The paper studies convex coradiant sets and their cogauges. While the concave gauge of a convex coradiant set is superlinear but discontinuous and its Minkowski cogauge is (possibly) continuous but is not concave, we are interested in those convex coradiant sets which admit a continuous concave cogauge. These sets are characterized in primal terms using their outer kernel and in dual terms using their reverse polar set. It is shown that a continuous concave cogauge, if it exists, is not unique; we prove that the class of continuous concave cogauges of some set C admits a greatest element and characterize its support set as the intersection of the reverse polar of C and the polar of its outer kernel.
Classification : 52A07, 46A55, 46B20
Mots-clés : Convex sets, concave gauge, cogauge, radiant sets, coradiant sets, reverse polar 
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     author = {A. Zaffaroni},
     title = {Convex {Coradiant} {Sets} with a {Continuous} {Concave} {Cogauge}},
     journal = {Journal of convex analysis},
     pages = {325--343},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2008},
     url = {http://geodesic.mathdoc.fr/item/JCA_2008_15_2_JCA_2008_15_2_a9/}
}
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A. Zaffaroni. Convex Coradiant Sets with a Continuous Concave Cogauge. Journal of convex analysis, Tome 15 (2008) no. 2, pp. 325-343. http://geodesic.mathdoc.fr/item/JCA_2008_15_2_JCA_2008_15_2_a9/