Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Alberto Zaffaroni

Dip. di Scienze Economiche e Matematico-Statistiche, Università del Salento, Centro Ecotekne, Via Monteroni, 73100 Lecce, Italy

azaffaroni@economia.unile.it

Keywords

  • Convex sets
  • concave gauge
  • cogauge
  • radiant sets
  • coradiant sets
  • reverse polar

Mathematics Subject Classification

52A07, 46A55, 46B20

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Suggested citation

A. Zaffaroni. “Convex Coradiant Sets with a Continuous Concave Cogauge.” Journal of Convex Analysis 15 (2008), No. 2, 325–343. https://doi.org/10.68381/jca15023

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Published by Heldermann Verlag, 2008. Rights now held by Banach Press LLC.