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UBC Theses and Dissertations

A robust linear program solver for projectahedra Laza, Marius

Abstract

Linear programming has a wide range of applications, optimization-related problems being one of them. Important concerns in linear programming are efficiency, robustness, and accuracy. Linear programming is used in a reachability analysis tool called Coho [GM99] for dynamical systems. Previous experience has shown that linear programs in this tool lead to highly ill-conditioned linear systems which prevented successful reachability analysis. This thesis presents a robust linear program solver with provable error bounds that exploits the special structure of the linear programs that result in the reachability tool. This contribution is of interest for the particular application for which it was developed. Furthermore, it shows how duality and combinatorial aspects of linear programming can be exploited to achieve greater efficiency, robustness, and accuracy.

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