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About Intrinsic Transversality of Pairs of Sets

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Abstract

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.

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Acknowledgements

The author thanks Nguyen Hieu Thao and the referees for the careful reading of the manuscript and constructive comments and suggestions.

The research was supported by Australian Research Council, project DP160100854.

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  1. Centre for Informatics and Applied Optimization, Federation University Australia, POB 663, Ballarat, VIC, 3350, Australia

    Alexander Y. Kruger

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  1. Alexander Y. Kruger
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Correspondence to Alexander Y. Kruger.

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Dedicated to the memory of Professor Jonathan Michael Borwein

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Kruger, A.Y. About Intrinsic Transversality of Pairs of Sets. Set-Valued Var. Anal 26, 111–142 (2018). https://doi.org/10.1007/s11228-017-0446-3

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