Computational Experience and the Explanatory Value of Condition Numbers for Linear Optimization

35 Pages Posted: 4 Feb 2002

See all articles by Robert M. Freund

Robert M. Freund

affiliation not provided to SSRN

Fernando Ordonez

University of Southern California - Epstein Department of Industrial & Systems Engineering

Date Written: January 2002

Abstract

The goal of this paper is to develop some computational experience and test the practical relevance of the theory of condition numbers C(d) for linear optimization, as applied to problem instances that one might encounter in practice. We used the NETLIB suite of linear optimization problems as a test bed for condition number computation and analysis. Our computational results indicate that 72% of the NETLIB suite problem instances are ill-conditioned. However, after pre-processing heuristics are applied, only 19% of the post-processed problem instances are ill-conditioned, and log C(d) of the finitely-conditioned post-processed problems is fairly nicely distributed. We also show that the number of IPM iterations needed to solve the problems in the NETLIB suite varies roughly linearly (and monotonically) with log C(d) of the post-processed problem instances. Empirical evidence yields a positive linear relationship between IPM iterations and log C(d) for the post-processed problem instances, significant at the 95% confidence level. Furthermore, 42% of the variation in IPM iterations among the NETLIB suite problem instances is accounted for by log C(d) of the problem instances after pre-processing.

Keywords: Convex Optimization, Complexity, Interior-Point Method, Barrier Method

Suggested Citation

Freund, Robert Michael and Ordonez, Fernando Ivan, Computational Experience and the Explanatory Value of Condition Numbers for Linear Optimization (January 2002). Available at SSRN: https://ssrn.com/abstract=299326 or http://dx.doi.org/10.2139/ssrn.299326

Robert Michael Freund (Contact Author)

affiliation not provided to SSRN

Fernando Ivan Ordonez

University of Southern California - Epstein Department of Industrial & Systems Engineering ( email )

United States
213-821-2413 (Phone)
213-740-1120 (Fax)

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