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- Title
Stationarity and Regularity of Infinite Collections of Sets.
- Authors
Kruger, Alexander; López, Marco
- Abstract
This article investigates extremality, stationarity, and regularity properties of infinite collections of sets in Banach spaces. Our approach strongly relies on the machinery developed for finite collections. When dealing with an infinite collection of sets, we examine the behavior of its finite subcollections. This allows us to establish certain primal-dual relationships between the stationarity/regularity properties some of which can be interpreted as extensions of the Extremal principle. Stationarity criteria developed in the article are applied to proving intersection rules for Fréchet normals to infinite intersections of sets in Asplund spaces.
- Subjects
SET theory; BANACH spaces; FRECHET spaces; EXTREMAL problems (Mathematics); FINITE groups
- Publication
Journal of Optimization Theory & Applications, 2012, Vol 154, Issue 2, p339
- ISSN
0022-3239
- Publication type
Article
- DOI
10.1007/s10957-012-0043-4