Strong CHIP, normality, and linear regularity of convex sets
نویسندگان
چکیده
منابع مشابه
Strong Chip, Normality, and Linear Regularity of Convex Sets
We extend the property (N) introduced by Jameson for closed convex cones to the normal property for a nite 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 proper...
متن کاملThe SECQ Linear Regularity and the Strong CHIP for In nite System of Closed Convex Sets in Normed Linear Spaces
We consider a nite or in nite family of closed convex sets with nonempty intersection in a normed space A property relating their epigraphs with their intersection s epigraph is studied and its relations to other constraint quali cations such as the linear regularity the strong CHIP and Jameson s G property are estab lished With suitable continuity assumption we show how this property can be en...
متن کاملThe SECQ, Linear Regularity, and the Strong CHIP for an Infinite System of Closed Convex Sets in Normed Linear Spaces
We consider a (finite or infinite) family of closed convex sets with nonempty intersection in a normed space. A property relating their epigraphs with their intersection’s epigraph is studied, and its relations to other constraint qualifications (such as the linear regularity, the strong CHIP, and Jameson’s (G)-property) are established. With suitable continuity assumption we show how this prop...
متن کاملBounded Linear Regularity, Strong CHIP, and CHIP are Distinct Properties
Bounded linear regularity, the strong conical hull intersection property (strong CHIP), and the conical hull intersection property (CHIP) are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. It was shown recently that these properties are fundamental in several branches of convex optimization, including convex feasibility problems, error bounds, Fe...
متن کاملStrong CHIP for Infinite System of Closed Convex Sets in Normed Linear Spaces
For a general (possibly infinite) system of closed convex sets in a normed linear space we provide several sufficient conditions for ensuring the strong conical hull intersection property. One set of sufficient conditions is given in terms of the finite subsystems while the other sets are in terms of the relaxed interior-point conditions together with appropriate continuity of the associated se...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2005
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-05-03945-0