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.
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Andersen, E.D., Mitchell, J.E., Roos, C., Terlaky, T. (2001). A Homogenized Cutting Plane Method to Solve the Convex Feasibility Problem. In: Yang, X., Teo, K.L., Caccetta, L. (eds) Optimization Methods and Applications. Applied Optimization, vol 52. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3333-4_10
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DOI: https://doi.org/10.1007/978-1-4757-3333-4_10
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