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Primal necessary characterizations of transversality properties

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Abstract

This paper continues the study of general nonlinear transversality properties of collections of sets and focuses on primal necessary (in some cases also sufficient) characterizations of the properties. We formulate geometric, metric and slope characterizations, particularly in the convex setting. The Hölder case is given a special attention. Quantitative relations between the nonlinear transversality properties of collections of sets and the corresponding regularity properties of set-valued mappings as well as two nonlinear transversality properties of a convex set-valued mapping to a convex set in the range space are discussed.

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Acknowledgements

We would like to thank the referees for the careful reading of the manuscript and their constructive comments and suggestions.

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Authors and Affiliations

  1. Centre for Informatics and Applied Optimization, School of Science, Engineering and Information Technology, Federation University Australia, POB 663, Ballarat, VIC, 3350, Australia

    Nguyen Duy Cuong & Alexander Y. Kruger

  2. Department of Mathematics, College of Natural Sciences, Can Tho University, Can Tho, Vietnam

    Nguyen Duy Cuong

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  1. Nguyen Duy Cuong
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  2. Alexander Y. Kruger
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Correspondence to Alexander Y. Kruger.

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The research was supported by the Australian Research Council, Project DP160100854. The second author benefited from the support of the FMJH Program PGMO and from the support of EDF.

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Cuong, N.D., Kruger, A.Y. Primal necessary characterizations of transversality properties. Positivity 25, 531–558 (2021). https://doi.org/10.1007/s11117-020-00775-5

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