Skip to main content
Log in

On a characterization of Clarke's tangent cone

  • Technical Note
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

For a subsetM of a normed vector spaceX, it is shown that, in the characterization given by Elster and Thierfelder of Clarke's tangent cone toM at a pointx 0X, there is a requirement which becomes superfluous whenx 0 belongs to the closure ofM.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Elster, K. H., andThierfelder, J.,A General Concept of Cone Approximations in Nondifferentiable Optimization, Nondifferentiable Optimization: Motivations and Applications, Edited by V. F. Demyanov and D. Pallaschke, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, Germany, Vol. 255, pp. 170–189, 1985.

    Google Scholar 

  2. Elster, K. H., andThierfelder, J.,Abstract Cone Approximations and Generalized Differentiability in Nonsmooth Optimization, Optimization, Vol. 19, pp. 315–341, 1988.

    Google Scholar 

  3. Elster, K. H., andThierfelder, J.,On Cone Approximations and Generalized Directional Derivatives, Nonsmooth Optimization and Related Topics, Edited by F. H. Clarke, V. F. Demyanov, and F. Giannessi, Plenum Press, New York, pp. 133–154, 1988.

    Google Scholar 

  4. Elster, K. H., andThierfelder, J.,Generalized Notions of Directional Derivatives, Research Paper No. 155, Applied Mathematics, Optimization, and Operations Research Section, Department of Mathematics, University of Pisa, 1988.

  5. Giorgi, G., andGuerraggio, A.,On the Notion of Tangent Cone in Mathematical Programming, Optimization (to appear).

  6. Aubin, J. P., andEkeland, I.,Applied Nonlinear Analysis, Wiley, New York, New York, 1984.

    Google Scholar 

  7. Laurent, P. J.,Approximation et Optimisation, Hermann, Paris, France, 1972.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by F. Giannessi

This research was supported by the Italian Ministry of University Scientific and Technological Research.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Giorgi, G., Guerraggio, A. On a characterization of Clarke's tangent cone. J Optim Theory Appl 74, 369–372 (1992). https://doi.org/10.1007/BF00940900

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00940900

Key Words

Navigation