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Comparison of Two Sets of First-Order Conditions as Bases of Interior-Point Newton Methods for Optimization with Simple Bounds

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  • D.C. Jamrog

    (Rice University)

  • R.A. Tapia

    (Rice University)

  • Y. Zhang

    (Rice University)

Abstract

In this paper, we compare the behavior of two Newton interior-point methods derived from two different first-order necessary conditions for the same nonlinear optimization problem with simple bounds. One set of conditions was proposed by Coleman and Li; the other is the standard KKT set of conditions. We discuss a perturbation of the CL conditions for problems with one-sided bounds and the difficulties involved in extending this to problems with general bounds. We study the numerical behavior of the Newton method applied to the systems of equations associated with the unperturbed and perturbed necessary conditions. Preliminary numerical results for convex quadratic objective functions indicate that, for this class of problems, the Newton method based on the perturbed KKT formulation appears to be the more robust.

Suggested Citation

  • D.C. Jamrog & R.A. Tapia & Y. Zhang, 2002. "Comparison of Two Sets of First-Order Conditions as Bases of Interior-Point Newton Methods for Optimization with Simple Bounds," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 21-40, April.
    • Handle: RePEc:spr:joptap:v:113:y:2002:i:1:d:10.1023_a:1014801112646
    DOI: 10.1023/A:1014801112646
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    References listed on IDEAS

    as
    1. C. Villalobos & R. Tapia & Y. Zhang, 2002. "Local Behavior of the Newton Method on Two Equivalent Systems from Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 239-263, February.
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