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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The authors thank the referees for the careful reading of the manuscript and constructive comments and suggestions.
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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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DOI: https://doi.org/10.1007/s11228-017-0436-5
Keywords
- Metric regularity
- Metric subregularity
- Transversality
- Subtransversality
- Intrinsic transversality
- Error bound
- Normal cone
- Alternating projections
- Linear convergence