- Title
- Stationarity and regularity of infinite collections of sets
- Creator
- Kruger, Alexander; López, Marco
- Date
- 2012
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/42647
- Identifier
- vital:4641
- Identifier
-
https://doi.org/10.1007/s10957-012-0043-4
- Identifier
- ISSN:0022-3239
- 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. © 2012 Springer Science+Business Media, LLC.
- Relation
- Journal of Optimization Theory and Applications Vol. 154, no. 2 (2012), p. 339-369; http://purl.org/au-research/grants/arc/DP110102011
- Rights
- Copyright Springer Science+Business Media, LLC.
- Rights
- Open Access
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0103 Numerical and Computational Mathematics; 0102 Applied Mathematics; 0906 Electrical and Electronic Engineering; Asplund space; Extremal principle; Extremality; Normal cone; Optimality; Regularity; Stationarity; Subdifferential
- Full Text
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