1,720,969 research outputs found
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
Tangentially ds-functions
No full textWe study functions whose directional derivatives can be written as a difference of two extended real-valued sublinear function (ds functions). The pair of convex sets obtained as the support functions of these sublinear functions is provided by a familiar equivalence relation and is considered as the bi-subdifferential of the function. We study calculus rules and give application to minimization problems
- …
