Regularity of collections of sets and convergence of inexact alternating projections
- Authors: Kruger, Alexander , Thao, Nguyen
- Date: 2016
- Type: Text , Journal article
- Relation: Journal of Convex Analysis Vol. 23, no. 3 (2016), p. 823-847
- Relation: http://purl.org/au-research/grants/arc/DP110102011
- Full Text: false
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- Description: We study the usage of regularity properties of collections of sets in convergence analysis of alternating projection methods for solving feasibility problems. Several equivalent characterizations of these properties are provided. Two settings of inexact alternating projections are considered and the corresponding convergence estimates are established and discussed.
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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- Reviewed:
- 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.