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New Complexity Analysis of the Primal—Dual Newton Method for Linear Optimization

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  • J. Peng
  • C. Roos
  • T. Terlaky

Abstract

We deal with the primal–dual Newton method for linear optimization (LO). Nowadays, this method is the working horse in all efficient interior point algorithms for LO, and its analysis is the basic element in all polynomiality proofs of such algorithms. At present there is still a gap between the practical behavior of the algorithms and the theoretical performance results, in favor of the practical behavior. This is especially true for so-called large-update methods. We present some new analysis tools, based on a proximity measure introduced by Jansen et al., in 1994, that may help to close this gap. This proximity measure has not been used in the analysis of large-update methods before. The new analysis does not improve the known complexity results but provides a unified way for the analysis of both large-update and small-update methods. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • J. Peng & C. Roos & T. Terlaky, 2000. "New Complexity Analysis of the Primal—Dual Newton Method for Linear Optimization," Annals of Operations Research, Springer, vol. 99(1), pages 23-39, December.
    • Handle: RePEc:spr:annopr:v:99:y:2000:i:1:p:23-39:10.1023/a:1019280614748
    DOI: 10.1023/A:1019280614748
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    Cited by:

    1. Peng, Jiming & Roos, Cornelis & Terlaky, Tamas, 2002. "A new class of polynomial primal-dual methods for linear and semidefinite optimization," European Journal of Operational Research, Elsevier, vol. 143(2), pages 234-256, December.

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