Skip to main content

Abstract

It is shown that exact estimates for local metric regularity are obtained with the help of the slope introduced by De Giorgi-Marino-Tosques in 1980. Interrelation between the slope and subdifferentials are further analyzed.

This research was partly supported by M.L. Bank Mathematics Research Fund.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Azé D., Corvellec J.-N., Lucchetti R. (1999) Variational pairs and applications to stability in non-smooth analysis, Nonlinear Ana1.TMA, to appear.

    Google Scholar 

  2. Borwein J., Zhu Q.J. (1999) A survey on subdifferential calculus, Nonlinear Anal. TMA 38: 687–773.

    Article  Google Scholar 

  3. Cominetti R. (1980) Metric regularity, tangent cones and second order optimality conditions, Applied Math. Optimization 21: 265–287

    Article  Google Scholar 

  4. De Giorgi E., Marino A., Tosques M. (1980) Problemi di evoluzione in spazi metrici a curve di massima pendenza, Atti Accad. Nat. Lincei, Rend. Cl. Sci Fiz. Mat. Natur. 68: 180–187.

    Google Scholar 

  5. Dmitruk A.V., Milyutin A.A., Osmolovskij N.P. (1980) Ljusternik theorem and theory of an extremum, Uspehi Mat. Nauk 35:6: 11–46 (in Russian). English translation: Russian Math. Survey 35:6: 11–51

    Google Scholar 

  6. Fabian M. (1989) Subdifferentiability and trustworthiness in the light of the new variational principle of Borwein and Preiss, Acta Univ. Carolinae 30: 5156.

    Google Scholar 

  7. Ioffe A.D. (1979) Regular points of Lipschitz functions, Trans. Amer. Math. Soc 251: 61–69.

    Article  Google Scholar 

  8. Ioffe A.D. (1987) Absolutely continuous subgradients of nonconvex integral functionals, Nonlinear Anal.TMA 11: 245–257.

    Article  Google Scholar 

  9. Ioffe A.D. (1987) On the local surjection property, Nonlinear Anal. TMA 11: 565–592.

    Article  Google Scholar 

  10. Ioffe A.D. (1996) Codirectional compactness, metric regularity and subdifferential calculus, in “Constructive, Experimental and Nonlinear Analysis (Limoges, 1999)”, Canad. Math. Soc. Proc. Ser., to appear.

    Google Scholar 

  11. Ioffe A.D. (1998) Trustworthiness and fuzzy principles, Set-Valued Analysis 6: 265–276.

    Article  Google Scholar 

  12. Jourani A. and Thibault L. (1995) Metric regularity and subdifferential calculus in Banach spaces, Set-Valued Analysis 3: 87–100.

    Article  Google Scholar 

  13. Lassonde M. (1999) First-order rules for nonsmooth constrained optimization, Nonlinear Anal. TMA, to appear.

    Google Scholar 

  14. Mordukhovich B.S. and Shao Yongheng (1996) Differential characterizations of covering, metric regularity and Lipschitzian properties of multifunctions between Banach spaces, Nonlinear Anal. TMA 25: 1401–1424.

    Article  Google Scholar 

  15. Zhu Q.J. (1998) The equivalence of several basic theorem on subdifferentials, Set-Valued Analysis 6: 171–185.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ioffe, A. (2001). Towards Metric Theory of Metric Regularity. In: Lassonde, M. (eds) Approximation, Optimization and Mathematical Economics. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57592-1_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-57592-1_15

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-1363-0

  • Online ISBN: 978-3-642-57592-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics