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About Subtransversality of Collections of Sets

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Abstract

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.

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Acknowledgements

The authors thank the referees for the careful reading of the manuscript and constructive comments and suggestions.

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Authors and Affiliations

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

    Alexander Y. Kruger

  2. Institut für Numerische und Angewandte Mathematik, Universität Göttingen, 37083, Göttingen, Germany

    D. Russell Luke & Nguyen H. Thao

  3. Department of Mathematics, Teacher College, Can Tho University, Can Tho City, Vietnam

    Nguyen H. Thao

Authors
  1. Alexander Y. Kruger
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  2. D. Russell Luke
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  3. Nguyen H. Thao
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Correspondence to Alexander Y. Kruger.

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Dedicated to Professor Michel Théra on the occasion of his 70th birthday

AYK was supported by Australian Research Council, project DP160100854. DRL was supported in part by German Israeli Foundation Grant G-1253-304.6 and Deutsche Forschungsgemeinschaft Research Training Grant 2088 TP-B5. NHT was supported by German Israeli Foundation Grant G-1253-304.6

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Kruger, A.Y., Luke, D.R. & Thao, N.H. About Subtransversality of Collections of Sets. Set-Valued Var. Anal 25, 701–729 (2017). https://doi.org/10.1007/s11228-017-0436-5

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