Bounded linear regularity, strong CHIP, and CHIP are distinct properties

Citation
Hh. Bauschke et al., Bounded linear regularity, strong CHIP, and CHIP are distinct properties, J CONVEX AN, 7(2), 2000, pp. 395-412
Citations number
25
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF CONVEX ANALYSIS
ISSN journal
0944-6532 → ACNP
Volume
7
Issue
2
Year of publication
2000
Pages
395 - 412
Database
ISI
SICI code
0944-6532(2000)7:2<395:BLRSCA>2.0.ZU;2-V
Abstract
Bounded linear regularity, the strong conical hull intersection property (s trong CHIP), and the conical hull intersection property (CHIP) are properti es of a collection of finitely many closed convex intersecting sets in Eucl idean space. It was shown recently that these properties are fundamental in several branches of convex optimization, including convex feasibility prob lems, error bounds, Fenchel duality, and constrained approximation. It was known that regularity implies strong CHIP. which ill turn implies CHIP; mor eover, the three properties always hold for subspaces. The question whether or not converse implications are true for general convex sets was open.