Skip to main content
SpringerLink
Log in

Separate Necessary and Sufficient Conditions for the Local Minimum of a Function

  • TECHNICAL NOTE
  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

This paper develops two necessary conditions for a local minimum of an arbitrary extended real-valued function (Theorem 2.2) and, quite separately, two conditions, each sufficient for such a function to have a strict local minimum (Theorem 2.3).

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • R. T. Rockafellar (1988) ArticleTitleFirst-Order and Second-Order Epidifferentiability in Nonlinear Programming. Transactions of the American Mathematical Society 307 75–108

    Google Scholar 

  • E. Goursat (Eds) (1813) Cours D’Analyse Mathématique Courcier Paris, France

    Google Scholar 

  • L. Qi (2001) ArticleTitleOn an Extended Lagrange Claim. Journal of Optimization Theory and Applications 108 685–688

    Google Scholar 

  • J. L. Lagrange (Eds) (1813) Thèorie des Fonctions Analytiques Courcier Paris, France

    Google Scholar 

  • A. Ben-Tal J. Zowe (1982) ArticleTitleNecessary and Sufficient Optimality Conditions for a Class of Nonsmooth Minimization Problems. Mathematical Programming 24 39–76

    Google Scholar 

  • L. R. Huang K. F. Ng (1994) ArticleTitleSecond-Order Necessary and Sufficient Conditions in Nonsmooth Optimization. Mathematical Programming 66 379–402

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Professor, Department of Mathematics, South China Normal University, Guang Zhou, PRC

    L. R. Huang

Authors
  1. L. R. Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was supported by the National Science Foundation of China, Grant 10171034, and the Natural Science Foundation of the Department of Education of Guangdong Province, Grant 820138.

The author thanks the referees for helpful comments.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huang, L. Separate Necessary and Sufficient Conditions for the Local Minimum of a Function. J Optim Theory Appl 125, 241–246 (2005). https://doi.org/10.1007/s10957-004-1726-2

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-004-1726-2

Keywords

Search

Navigation