Strong CHIP, normality, and linear regularity of convex sets
| Autor: | Andrew Bakan, Frank Deutsch, Wu Li |
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| Rok vydání: | 2005 |
| Předmět: | |
| Zdroj: | Transactions of the American Mathematical Society. 357:3831-3863 |
| ISSN: | 1088-6850 0002-9947 |
| Popis: | We extend the property (N) introduced by Jameson for closed convex cones to the normal property for a finite collection of convex sets in a Hilbert space. Variations of the normal property, such as the weak normal property and the uniform normal property, are also introduced. A dual form of the normal property is derived. When applied to closed convex cones, the dual normal property is the property (G) introduced by Jameson. Normality of convex sets provides a new perspective on the relationship between the strong conical hull intersection property (strong CHIP) and various regularity properties. In particular, we prove that the weak normal property is a dual characterization of the strong CHIP, and the uniform normal property is a. characterization of the linear regularity. Moreover, the linear regularity is equivalent to the fact that the normality constant for feasible direction cones of the convex sets at x is bounded away from 0 uniformly over all points in the intersection of these convex sets. |
| Databáze: | OpenAIRE |
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