28 research outputs found
Conically equivalent convex sets and applications
No full textGiven 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
No full textGiven a normed space X and a cone K μ 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
No full textGiven 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
Primal worst and dual best in robust vector optimization
No full textWe establish a relationship between the robust counterpart of an uncertain cone-convex vector problem and the optimistic counterpart of its uncertain dual. Along the line marked by Beck and Ben-Tal (2009) in the scalar case, we show that operating in the primal problem with a pessimistic view is equivalent to operating with an optimistic approach in its dual
