Skip to main content
SpringerLink
Log in

A numerical investigation of rank-two ellipsoid algorithms for nonlinear programming

  • Published:
Mathematical Programming Submit manuscript

Abstract

We study the performance of some rank-two ellipsoid algorithms when used to solve nonlinear programming problems. Experiments are reported which show that the rank-two algorithms studied are slightly less efficient than the usual rank-one (center-cut) algorithm. Some results are also presented concerning the growth of ellipsoid asphericity in rank-one and rank-two algorithms.

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. R.G. Bland, D. Goldfarb and M.J. Todd, “The ellipsoid method: a survey,”Operations Research 29 (1981) 1039–1091.

    Google Scholar 

  2. A.R. Colville, “A comparative study on nonlinear programming codes,” IBM New York Scientific Center Report 320-2949, International Business Machines Corporation (New York, 1968).

    Google Scholar 

  3. R.S. Dembo, “A set of geometric programming test problems and their solutions,”Mathematical Programming 10 (1976) 192–213.

    Google Scholar 

  4. A. Ech-cherif, “Rank-two and variable bounds ellipsoid algorithms for convex programming,” Ph.D. Dissertation, Rennsselaer Polytechnic Institute (Troy, NY, 1985).

    Google Scholar 

  5. A. Ech-cherif and J.G. Ecker, “A class of rank-two ellipsoid algorithms for convex programming,”Mathematical Programming 29 (1984) 187–202.

    Google Scholar 

  6. J.G. Ecker and M. Kupferschmid, “An ellipsoid algorithm for nonlinear programming,”Mathematical Programming 27 (1983) 83–106.

    Google Scholar 

  7. J.G. Ecker and M. Kupferschmid, “A computational comparison of the ellipsoid algorithm with several nonlinear programming algorithms,”SIAM Journal on Control and Optimization 23 (1985).

  8. D.B. Iudin and A.S. Nemirovskii, “Informational complexity and effective methods for solving convex extremal problems,”Matekon 13 (1977) 25–45.

    Google Scholar 

  9. B. Korte and R. Schrader, “Can the ellipsoid method be efficient?,” Report No. 81177-OR, Institut für Okonometrie und Operations Research, Universität Bonn, January 1981.

  10. N.Z. Shor, “Cut-off method with space extension in convex programming problems,”Cybernetics 13 (1977) 881–886.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, General Motors Research Laboratories, 48090, Warren, MI, USA

    A. Ech-Cherif

  2. Mathematical Sciences Department, Rennsselaer Polytechnic Institute, 12180-3590, Troy, NY, USA

    J. G. Ecker

  3. Alan M. Voorhees Computing Center, and Program in Operations Research and Statistics, Rennsselaer Polytechnic Institute, 2180-3590, Troy, NY, USA

    Michael Kupferschmid

Authors
  1. A. Ech-Cherif
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. G. Ecker
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael Kupferschmid
    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

Ech-Cherif, A., Ecker, J.G. & Kupferschmid, M. A numerical investigation of rank-two ellipsoid algorithms for nonlinear programming. Mathematical Programming 43, 87–95 (1989). https://doi.org/10.1007/BF01582280

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01582280

Key words

Search

Navigation