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Computational and Analytical Mathematics pp 365–374Cite as

On Derivative Criteria for Metric Regularity

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 50))

Abstract

We give a simple self-contained proof of the equality which links directly the graphical derivative and coderivative criteria for metric regularity. Then we present a sharper form of the criterion for strong metric regularity involving the paratingent derivative.

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References

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Acknowledgements

ALD was partially supported by the National Science Foundation Grant DMS-1008341 through the University of Michigan. HF was partially supported by the European Union under the 7th Framework Programme FP7-PEOPLE-2010-ITN. Grant agreement number 264735-SADCO.

Author information

Authors and Affiliations

  1. Mathematical Reviews, 416 Fourth Street, Ann Arbor, MI, 48107-8604, USA

    Asen L. Dontchev

  2. CNRS, Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie, 4 place Jussieu, 75252, Paris, France

    Hélène Frankowska

Authors
  1. Asen L. Dontchev
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  2. Hélène Frankowska
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Corresponding author

Correspondence to Asen L. Dontchev .

Editor information

Editors and Affiliations

  1. Lawrence Berkeley National Laboratory, Berkeley, USA

    David H. Bailey

  2. Mathematics, University of British Columbia, Kelowna, British Columbia, Canada

    Heinz H. Bauschke

  3. Dept. Mathematics & Statistics, Simon Fraser University, Burnaby, British Columbia, Canada

    Peter Borwein

  4. Mathematics, University of Florida, Gainesville, Florida, USA

    Frank Garvan

  5. Mathematics and Computer Science, University of Limoges, Limoges, France

    Michel Théra

  6. Mathematics and Computer Science Department, La Sierra University, Riverside, California, USA

    Jon D. Vanderwerff

  7. Dept. Combinatorics & Optimization, University of Waterloo Faculty of Mathematics, Waterloo, Ontario, Canada

    Henry Wolkowicz

Additional information

Communicated by Heinz H. Bauschke.

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Dontchev, A.L., Frankowska, H. (2013). On Derivative Criteria for Metric Regularity. In: Bailey, D., et al. Computational and Analytical Mathematics. Springer Proceedings in Mathematics & Statistics, vol 50. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7621-4_16

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