About intrinsic transversality of pairs of sets
- Authors: Kruger, Alexander
- Date: 2018
- Type: Text , Journal article
- Relation: Set-Valued and Variational Analysis Vol. 26, no. 1 (2018), p. 111-142
- Relation: http://purl.org/au-research/grants/arc/DP160100854
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- Description: The article continues the study of the ‘regular’ arrangement of a collection of sets near a point in their intersection. Such regular intersection or, in other words, transversality properties are crucial for the validity of qualification conditions in optimization as well as subdifferential, normal cone and coderivative calculus, and convergence analysis of computational algorithms. One of the main motivations for the development of the transversality theory of collections of sets comes from the convergence analysis of alternating projections for solving feasibility problems. This article targets infinite dimensional extensions of the intrinsic transversality property introduced recently by Drusvyatskiy, Ioffe and Lewis as a sufficient condition for local linear convergence of alternating projections. Several characterizations of this property are established involving new limiting objects defined for pairs of sets. Special attention is given to the convex case.
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.