Journal of Convex Analysis 15 (2008), No. 2, 325--343
Copyright Heldermann Verlag 2008
Convex Coradiant Sets with a Continuous Concave Cogauge
Alberto Zaffaroni
Dip. di Scienze Economiche e Matematico-Statistiche, Università del Salento, Centro Ecotekne, Via Monteroni, 73100 Lecce, Italy
azaffaroni@economia.unile.it
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.
Keywords: Convex sets, concave gauge, cogauge, radiant sets, coradiant sets, reverse polar.
MSC: 52A07, 46A55, 46B20
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