Given a normed space X and a cone K in X, two closed, convex sets A and B in X* are said to be K-equivalent if the support functions of A and B coincide on K. We characterize the greatest set in an equivalence class, analyze the equivalence between two sets, find conditions for the existence and the uniqueness of a minimal set, extending previous results. We give some applications to the study of gauges of convex radiant sets and of cogauges of convex coradiant sets. Moreover we study the minimality of a second order hypodifferential.
Conically equivalent convex sets and applications / Elisa, Caprari; Zaffaroni, Alberto. - In: PACIFIC JOURNAL OF OPTIMIZATION. - ISSN 1348-9151. - STAMPA. - 6:2(2010), pp. 281-303.
Conically equivalent convex sets and applications
ZAFFARONI, Alberto
2010
Abstract
Given a normed space X and a cone K in X, two closed, convex sets A and B in X* are said to be K-equivalent if the support functions of A and B coincide on K. We characterize the greatest set in an equivalence class, analyze the equivalence between two sets, find conditions for the existence and the uniqueness of a minimal set, extending previous results. We give some applications to the study of gauges of convex radiant sets and of cogauges of convex coradiant sets. Moreover we study the minimality of a second order hypodifferential.
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