A Homogenized Cutting Plane Method To Solve The Convex Feasibility Problem (1999)
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BibTeX
@MISC{Andersen99ahomogenized,
author = {E. D. Andersen and J. E. Mitchell and C. Roos and T. Terlaky and Tu Delft},
title = {A Homogenized Cutting Plane Method To Solve The Convex Feasibility Problem},
year = {1999}
}
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Abstract
: We present a cutting plane algorithm for the feasibility problem that uses a homogenized self-dual approach to regain an approximate center when adding a cut. The algorithm requires a fully polynomial number of Newton steps. One novelty in the analysis of the algorithm is the use of a powerful proximity measure which is widely used in interior point methods but not previously used in the analysis of cutting plane methods. Moreover, a practical implementation of a variant of the homogenized cutting plane for solution of LPs is presented. Computational results with this implementation show that it is possible to solve a problem having several thousand constraints and about one million variables on a standard PC in a moderate amount of time. Key words: Interior-point, Homogeneous, cutting plane, set-partitioning. Permanent address: Math Sciences, RPI, Troy NY 12180, USA. Supported in part by fellowships from NWO and TU Delft 1 2 1 INTRODUCTION We are trying to nd a point y in a...
