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

Title: Bounded linear regularity, strong CHIP, and CHIP are distinct properties
Creator: Bauschke, Heinz H.; Borwein, Jonathan M.; Tseng, Paul
Relation: Journal of Convex Analysis Vol. 7, Issue 2, p. 395-412
Relation: http://www.emis.de/journals/JCA/vol.7_no.2/9.html
Publisher: Heldermann Verlag
Resource Type: journal article
Date: 2000
Description: 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, Fenchel duality, and constrained approximation. It was known that regularity implies strong CHIP, which in turn implies CHIP; moreover, the three properties always hold for subspaces. The question whether or not converse implications are true for general convex sets was open. We show that - even for convex cones - the converse implications need not hold by constructing counter-examples in ℝ⁴.
Subject: bounded linear regularity; linear regularity; normal cone; property CHIP; property strong CHIP; tangent cone
Identifier: http://hdl.handle.net/1959.13/940664
Identifier: uon:13063
Identifier: ISSN:0944-6532
Language: eng
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