[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

On conditions to have bounded multipliers in locally lipschitz programming

  • Short Communication
  • Published:
Mathematical Programming Submit manuscript

Abstract

For a nonlinear programming problem with locally Lipschitz objective and inequality constraint functions and continuously differentiable equality constraint functions, a necessary and sufficient condition is presented for the set of multiplier vectors to be nonempty and bounded.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

References

  1. F.H. Clarke, “Generalized gradients and applications”,Transactions of the American Mathematical Society 205 (1975) 247–262.

    Google Scholar 

  2. J. Gauvin, “A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programming”,Mathematical Programming 12 (1977) 136–138.

    Google Scholar 

  3. J. Gauvin and J.W. Tolle, “Differential stability in nonlinear programming”,SIAM Journal on Control and Optimization 15 (1977) 294–311.

    Google Scholar 

  4. J.-B. Hiriart-Urruty, “On optimality conditions in nondifferentiable programming”,Mathematical Programming 14 (1978) 73–86.

    Google Scholar 

  5. O.L. Mangasarian and S. Fromovitz, “The Fritz John necessary optimality condition in the presence of equality and inequality constraints”,Journal of Mathematical Analysis and Applications 17 (1967) 37–47.

    Google Scholar 

  6. R.T. Rockafellar, “Clarke's tangent cones and the boundaries of closed sets inR n”,Nonlinear Analysis 3 (1979) 145–154.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Mathématique, Facultes Universitaires de Namur, Namur, Belgium

    V. Hien Nguyen & J. -J. Strodiot

  2. Washington State University, Pullman, WA, USA

    R. Mifflin

Authors
  1. V. Hien Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. -J. Strodiot
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Mifflin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This author's work was supported by the National Science Foundation under Grant No. MCS 78-06716.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nguyen, V.H., Strodiot, J.J. & Mifflin, R. On conditions to have bounded multipliers in locally lipschitz programming. Mathematical Programming 18, 100–106 (1980). https://doi.org/10.1007/BF01588302

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01588302

Key words

Search

Navigation