Advertisement

Towards Metric Theory of Metric Regularity

  • Alexander Ioffe

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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. 2.
    Borwein J., Zhu Q.J. (1999) A survey on subdifferential calculus, Nonlinear Anal. TMA 38: 687–773.CrossRefGoogle Scholar
  3. 3.
    Cominetti R. (1980) Metric regularity, tangent cones and second order optimality conditions, Applied Math. Optimization 21: 265–287CrossRefGoogle Scholar
  4. 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. 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: 11–51Google Scholar
  6. 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. 7.
    Ioffe A.D. (1979) Regular points of Lipschitz functions, Trans. Amer. Math. Soc 251: 61–69.CrossRefGoogle Scholar
  8. 8.
    Ioffe A.D. (1987) Absolutely continuous subgradients of nonconvex integral functionals, Nonlinear Anal.TMA 11: 245–257.CrossRefGoogle Scholar
  9. 9.
    Ioffe A.D. (1987) On the local surjection property, Nonlinear Anal. TMA 11: 565–592.CrossRefGoogle Scholar
  10. 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. 11.
    Ioffe A.D. (1998) Trustworthiness and fuzzy principles, Set-Valued Analysis 6: 265–276.CrossRefGoogle Scholar
  12. 12.
    Jourani A. and Thibault L. (1995) Metric regularity and subdifferential calculus in Banach spaces, Set-Valued Analysis 3: 87–100.CrossRefGoogle Scholar
  13. 13.
    Lassonde M. (1999) First-order rules for nonsmooth constrained optimization, Nonlinear Anal. TMA, to appear.Google Scholar
  14. 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.CrossRefGoogle Scholar
  15. 15.
    Zhu Q.J. (1998) The equivalence of several basic theorem on subdifferentials, Set-Valued Analysis 6: 171–185.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Alexander Ioffe
    • 1
  1. 1.Department of MathematicsTechnionHaifaIsrael

Personalised recommendations