Skip to main content
SpringerLink
Log in

Second-order sufficient optimality conditions for local and global nonlinear programming

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

This paper presents a new approach to the sufficient conditions of nonlinear programming. Main result is a sufficient condition for the global optimality of a Kuhn-Tucker point. This condition can be verified constructively, using a novel convexity test based on interval analysis, and is guaranteed to prove global optimality of strong local minimizers for sufficiently narrow bounds. Hence it is expected to be a useful tool within branch and bound algorithms for global optimization.

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

  1. Fletcher, R. (1987), Practical Methods of Optimization, 2nd ed., Wiley, Chichester.

    Google Scholar 

  2. Horst, R. and Tuy, H. (1990), Global Optimization: Deterministic Approaches, 2nd ed., Springer, Berlin, 1990.

    Google Scholar 

  3. Horst, R. Pardalos, P.M. and Thoai, N.V. (1995), Introduction to Global Optimization, Kluwer, Dordrecht 1995.

    Google Scholar 

  4. John, F. (1985), pp. 543–560 in: Fritz John, Collected Papers, Vol. 2, Extremum problems with inequalities as subsidiary conditions (J.Moser, ed.), Birkhäuser, Boston, 543–560.

    Google Scholar 

  5. Karush, W. (1939), Minima of Functions of Several Variables with Inequalitis as Side Constraints, M.Sc. Dissertation, Dept. of Mathematics, Univ. of Chicago, Chicago, Illinois.

  6. Kuhn, H.W. and Tucker, A.W. (1951) pp. 481–492 in: Nonlinear Programming, Proc. 2nd Berkeley Symp. Math. Stat. Prob. (J.Neyman, ed.), Univ. of California Press, Berkeley, California.

    Google Scholar 

  7. Lagrange, J.L. (1797), Théorie des fonctions analytiques, Impr. de la République, Paris

    Google Scholar 

  8. Neumaier, A. (1990), Interval Methods for Systems of Equations, Cambridge Univ. Press, Cambridge.

    Google Scholar 

  9. Neumaier, A. (1992) An optimality criterion for global quadratic optimization, J. Global Optimization 2, 201–208.

    Google Scholar 

  10. Pardalos, P.M. and Schnitger, G. (1988), Checking local optimality in constrained quadratic programming is NP-hard, Oper. Res. Lett. 7, 33–35.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. AT&T Bell Laboratories, 600 Mountain Avenue, 07974-0636, Murray Hill, NJ, U.S.A.

    Arnold Neumaier

Authors
  1. Arnold Neumaier
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Neumaier, A. Second-order sufficient optimality conditions for local and global nonlinear programming. J Glob Optim 9, 141–151 (1996). https://doi.org/10.1007/BF00121660

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00121660

Key words

Mathematics Subject Classifications (1991)

Search

Navigation