A new condition number for linear programming

Abstract.

In this paper we define a new condition number ?(A) for the following problem: given a m by n matrix A, find x∈ℝⁿ, s.t. Ax<0. We characterize this condition number in terms of distance to ill-posedness and we compare it with existing condition numbers for the same problem.

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1. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, e-mail: {50000548@plink,macucker@math}.cityu.edu.hk, , , , , , HK

   Dennis Cheung & Felipe Cucker

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1. Dennis Cheung
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2. Felipe Cucker
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Received: November 5, 1999 / Accepted: November 2000¶Published online September 17, 2001

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Cheung, D., Cucker, F. A new condition number for linear programming. Math. Program. 91, 163–174 (2001). https://doi.org/10.1007/s101070100237

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• Issue Date: October 2001

• DOI: https://doi.org/10.1007/s101070100237

• Mathematics Subject Classification (2000): 90C05