Set regularities and feasibility problems
- Authors: Kruger, Alexander , Luke, Russell , Thao, Nguyen
- Date: 2018
- Type: Text , Journal article
- Relation: Mathematical Programming Vol. 168, no. 1-2 (2018), p. 279-311
- Relation: http://purl.org/au-research/grants/arc/DP160100854
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- Description: We synthesize and unify notions of regularity, both of individual sets and of collections of sets, as they appear in the convergence theory of projection methods for consistent feasibility problems. Several new characterizations of regularities are presented which shed light on the relations between seemingly different ideas and point to possible necessary conditions for local linear convergence of fundamental algorithms
About subtransversality of collections of sets
- Authors: Kruger, Alexander , Luke, Russell , Thao, Nguyen
- Date: 2017
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 25, no. 4 (2017), p. 701-729
- Relation: http://purl.org/au-research/grants/arc/DP160100854
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- Description: We provide dual sufficient conditions for subtransversality of collections of sets in an Asplund space setting. For the convex case, we formulate a necessary and sufficient dual criterion of subtransversality in general Banach spaces. Our more general results suggest an intermediate notion of subtransversality, what we call weak intrinsic subtransversality, which lies between intrinsic transversality and subtransversality in Asplund spaces.