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Quantitative Characterizations of Regularity Properties of Collections of Sets

Journal of Optimization Theory and Applications volume 164, pages 41–67 (2015)Cite this article

Abstract

Several primal and dual quantitative characterizations of regularity properties of collections of sets in normed linear spaces are discussed. Relationships between regularity properties of collections of sets and those of set-valued mappings are provided.

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Notes

  1. Observed by a reviewer.

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Acknowledgments

The authors wish to thank the referees for their very careful reading of the paper and many valuable comments and suggestions, which helped us improve the presentation. The authors also thank Editor-in-Chief Professor Franco Giannessi for his time and patience when scrutinizing this paper. The research was supported by the Australian Research Council, project DP110102011.

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Authors and Affiliations

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

    Alexander Y. Kruger & Nguyen H. Thao

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  1. Alexander Y. Kruger
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  2. Nguyen H. Thao
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Correspondence to Alexander Y. Kruger.

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Kruger, A.Y., Thao, N.H. Quantitative Characterizations of Regularity Properties of Collections of Sets. J Optim Theory Appl 164, 41–67 (2015). https://doi.org/10.1007/s10957-014-0556-0

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  • DOI: https://doi.org/10.1007/s10957-014-0556-0

Keywords

  • Collections of sets
  • Metric regularity
  • Normal cone
  • Subdifferential

Mathematics Subject Classification (2000)

  • 49J53
  • 49K27
  • 58E30