Stationarity and Regularity of Infinite Collections of Sets

Alexander Y. Kruger () and Marco A. López ()
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Alexander Y. Kruger: University of Ballarat
Marco A. López: University of Ballarat

Journal of Optimization Theory and Applications, 2012, vol. 154, issue 2, No 2, 339-369

Abstract: 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.

Keywords: Subdifferential; Normal cone; Optimality; Extremality; Stationarity; Regularity; Extremal principle; Asplund space (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-012-0043-4

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