Geodesic
Bounded Linear Regularity, Strong CHIP, and CHIP are Distinct Properties
Journal of convex analysis, Tome 7 (2000) no. 2, pp. 395-412

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 90C25, 46C05, 52A15, 52A20
Mots-clés : Bounded linear regularity, linear regularity, normal cone, property CHIP, property strong CHIP, tangent cone 
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     author = {H. H. Bauschke and J. M. Borwein and P. Tseng},
     title = {Bounded {Linear} {Regularity,} {Strong} {CHIP,} and {CHIP} are {Distinct} {Properties}},
     journal = {Journal of convex analysis},
     pages = {395--412},
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H. H. Bauschke; J. M. Borwein; P. Tseng. Bounded Linear Regularity, Strong CHIP, and CHIP are Distinct Properties. Journal of convex analysis, Tome 7 (2000) no. 2, pp. 395-412. http://geodesic.mathdoc.fr/item/JCA_2000_7_2_JCA_2000_7_2_a8/