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Probabilistic Analysis of Condition Numbers for Linear Programming

Author

Listed:
  • D. Cheung

    (City University of Hong Kong)

  • F. Cucker

    (City University of Hong Kong)

Abstract

In this paper, we provide bounds for the expected value of the log of the condition number C(A) of a linear feasibility problem given by a n × m matrix A (Ref. 1). We show that this expected value is O(min{n, m log n}) if n > m and is O(log n) otherwise. A similar bound applies for the log of the condition number C R(A) introduced by Renegar (Ref. 2).

Suggested Citation

  • D. Cheung & F. Cucker, 2002. "Probabilistic Analysis of Condition Numbers for Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 114(1), pages 55-67, July.
    • Handle: RePEc:spr:joptap:v:114:y:2002:i:1:d:10.1023_a:1015460004163
    DOI: 10.1023/A:1015460004163
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    References listed on IDEAS

    as
    1. Yinyu Ye, 1994. "Toward Probabilistic Analysis of Interior-Point Algorithms for Linear Programming," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 38-52, February.
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