Skip to main content

Interior-Point Methods for Nonconvex Nonlinear Programming: Filter Methods and Merit Functions

Computational Optimization and Applications volume 23, pages 257–272 (2002)Cite this article

Abstract

Recently, Fletcher and Leyffer proposed using filter methods instead of a merit function to control steplengths in a sequential quadratic programming algorithm. In this paper, we analyze possible ways to implement a filter-based approach in an interior-point algorithm. Extensive numerical testing shows that such an approach is more efficient than using a merit function alone.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

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

References

  1. A.R. Conn, N. Gould, and Ph.L. Toint, “Constrained and unconstrained testing environment,” available at http://www.dci.clrc.ac.uk/Activity.asp?CUTE

  2. E.D. Dolan and J.J. Moré, “Benchmarking optimization software with performance profiles,” Technical report, Argonne National Laboratory, January 2001.

  3. A.V. Fiacco and G.P. McCormick, Nonlinear Programming: Sequential Unconstrainted Minimization Techniques. Research Analysis Corporation, McLeanVirginia, 1968 (Republished in 1990 by SIAM, Philadelphia).

    Google Scholar 

  4. R. Fletcher and S. Leyffer, “Nonlinear programming without a penalty function,” Technical Report NA/171, University of Dundee, Dept. of Mathematics, Dundee, Scotland, 1997.

    Google Scholar 

  5. R. Fourer, D.M. Gay, and B.W. Kernighan, AMPL: A Modeling Language for Mathematical Programming, Scientific Press, 1993.

  6. K. Schittkowski, More Test Samples for Nonlinear Programming Codes, Springer Verlag: New York, 1987.

    Google Scholar 

  7. D.F. Shanno, H.Y. Benson, and R.J. Vanderbei, “Interior-point methods for nonconvex nonlinear programming: Filter methods and merit functions,” Technical Report ORFE 00-06, Department of Operations Research and Financial Engineering, Princeton University, 2000.

  8. D.F. Shanno and R.J. Vanderbei, “Interior-point methods for nonconvex nonlinear programming: Orderings and higher-order methods,” Math. Prog., vol. 87, no. 2, pp. 303–316, 2000.

    Google Scholar 

  9. R.J. Vanderbei, AMPL models, available at http://www.sor.princeton.edu/~rvdb/ampl/nlmodels

  10. R.J. Vanderbei, “LOQO: An interior point code for quadratic programming,” Optimization Methods and Software, vol. 12, pp. 451–484, 1999.

    Google Scholar 

  11. R.J. Vanderbei and D.F. Shanno, “An interior-point algorithm for nonconvex nonlinear programming,” Computational Optimization and Applications,” vol. 13, pp. 231–252, 1999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Operations Research and Financial Engineering, Princeton University, Princeton, NJ, USA

    Hande Y. Benson & Robert J. Vanderbei

  2. Rutgers University, New Brunswick, NJ, USA

    David F. Shanno

Authors
  1. Hande Y. Benson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Robert J. Vanderbei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David F. Shanno
    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

Benson, H.Y., Vanderbei, R.J. & Shanno, D.F. Interior-Point Methods for Nonconvex Nonlinear Programming: Filter Methods and Merit Functions. Computational Optimization and Applications 23, 257–272 (2002). https://doi.org/10.1023/A:1020533003783

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020533003783

  • interior-point methods
  • nonconvex optimization
  • nonlinear programming
  • filter methods