Quantitative characterizations of regularity properties of collections of sets
- Authors: Kruger, Alexander , Thao, Nguyen
- Date: 2015
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 164, no. 1 (2015), p. 41-67
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: Several primal and dual quantitative characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of collections of sets and those of set-valued mappings are provided.
About [q]-regularity properties of collections of sets
- Authors: Kruger, Alexander , Thao, Nguyen
- Date: 2014
- Type: Text , Journal article
- Relation: Journal of Mathematical Analysis and Applications Vol. 416, no. 2 (2014), p. 471-496
- Relation: http://purl.org/au-research/grants/arc/DP110102011
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- Description: We examine three primal space local Holder 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.
- Description: We examine three primal space local Holder 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. (C) 2014 Elsevier Inc. All rights reserved.