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On Central-Path Proximity Measures in Interior-Point Methods

Author

Listed:
  • M. D. Gonzalez-Lima

    (Simón Bolívar University, Texas A&M University of Corpus Christi)

  • C. Roos

    (Delft University of Technology)

Abstract

One of the main ingredients of interior-point methods is the generation of iterates in a neighborhood of the central path. Measuring how close the iterates are to the central path is an important aspect of such methods and it is accomplished by using proximity measure functions. In this paper, we propose a unified presentation of the proximity measures and a study of their relationships and computational role when using a generic primal-dual interior-point method for computing the analytic center for a standard linear optimization problem. We demonstrate that the choice of the proximity measure can affect greatly the performance of the method. It is shown that we may be able to choose the algorithmic parameters and the central-path neighborhood radius (size) in such a way to obtain comparable results for several measures. We discuss briefly how to relate some of these results to nonlinear programming problems.

Suggested Citation

  • M. D. Gonzalez-Lima & C. Roos, 2005. "On Central-Path Proximity Measures in Interior-Point Methods," Journal of Optimization Theory and Applications, Springer, vol. 127(2), pages 303-328, November.
    • Handle: RePEc:spr:joptap:v:127:y:2005:i:2:d:10.1007_s10957-005-6541-x
    DOI: 10.1007/s10957-005-6541-x
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    Cited by:

    1. Roger Behling & Clovis Gonzaga & Gabriel Haeser, 2014. "Primal-Dual Relationship Between Levenberg–Marquardt and Central Trajectories for Linearly Constrained Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 705-717, September.

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