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Stationarity and Regularity of Set Systems

Alexander Kruger (a.kruger***at***ballarat.edu.au)

Abstract: Extremality, stationarity and regularity notions for a system of closed sets in a normed linear space are investigated. The equivalence of different abstract "extremal" settings in terms of set systems and multifunctions is proved. The dual necessary and sufficient conditions of weak stationarity (the Extended extremal principle) are presented for the case of an Asplund space.

Keywords: nonsmooth analysis, normal cone, optimality, extremality, stationarity, regularity, set-valued mapping, Asplund space

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: University of Ballarat, School of Information Technology and Mathematical Sciences, Research Report 04/13. Published in Pacific J. Optimization, 2005, v. 1, 101-126.

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Entry Submitted: 06/21/2004
Entry Accepted: 06/26/2004
Entry Last Modified: 02/07/2005

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