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Solving linear programs with finite precision: I. Condition numbers and random programs

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Abstract.

We define a condition number (A,b,c) for a linear program min x s.t. Ax=b,x≥0 and give two characterizations via distances to degeneracy and singularity. We also give bounds for the expected value, as well as for higher moments, of log (A,b,c) when the entries of A,b and c are i.i.d. random variables with normal distribution.

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Authors and Affiliations

  1. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong

    Dennis Cheung & Felipe Cucker

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  1. Dennis Cheung
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  2. Felipe Cucker
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Correspondence to Dennis Cheung.

Additional information

This work has been substantially funded by a grant from the Research Grants Council of the Hong Kong SAR (project number CityU 1085/02P)

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Cheung, D., Cucker, F. Solving linear programs with finite precision: I. Condition numbers and random programs. Math. Program., Ser. A 99, 175–196 (2004). https://doi.org/10.1007/s10107-003-0393-7

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  • DOI: https://doi.org/10.1007/s10107-003-0393-7

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