Probabilistic Analysis of Condition Numbers for Linear Programming

D. Cheung and F. Cucker
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D. Cheung: City University of Hong Kong
F. Cucker: City University of Hong Kong

Journal of Optimization Theory and Applications, 2002, vol. 114, issue 1, No 3, 55-67

Abstract: 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).

Keywords: linear programming; condition numbers; probabilistic analysis of algorithms (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1015460004163

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