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About [q]-regularity properties of collections of sets

Alexander Y. Kruger (a.kruger***at***ballarat.edu.au)
Nguyen H. Thao (hieuthaonguyen***at***students.ballarat.edu.au)

Abstract: We examine three primal space local Hoelder type regularity properties of finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and uniform [q]-regularity as well as their quantitative characterizations. Equivalent metric characterizations of the three mentioned regularity properties as well as a sufficient condition of [q]-subregularity in terms of Frechet normals are established. The relationships between [q]-regularity properties of collections of sets and the corresponding regularity properties of set-valued mappings are discussed.

Keywords: Metric regularity; Uniform regularity; Normal cone; Subdifferential

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: Journal of Mathematical Analysis and Applications. http://dx.doi.org/10.1016/j.jmaa.2014.02.028

Download: [PDF]

Entry Submitted: 10/21/2013
Entry Accepted: 10/21/2013
Entry Last Modified: 03/31/2014

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