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Combining phase I and phase II in a potential reduction algorithm for linear programming

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Abstract

This paper describes an affine potential reduction algorithm for linear programming that simultaneously seeks feasibility and optimality. The algorithm is closely related to a similar method of Anstreicher. The new features are that we use a two-dimensional programming problem to derive better lower bounds than Anstreicher, that our direction-finding subproblem treats phase I and phase II more symmetrically, and that we do not need an initial lower bound. Our method also allows for the generation of a feasible solution (so that phase I is terminated) during the course of the iterations, and we describe two ways to encourage this behavior.

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Authors and Affiliations

  1. School of Operations Research and Industrial Engineering, Cornell University, 14853-7501, Ithaca, NY, USA

    Michael J. Todd

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  1. Michael J. Todd
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Research supported in part by NSF grant DMS-8904406 and by NSF, AFOSR and ONR through NSF grant DMS-8920550.

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Todd, M.J. Combining phase I and phase II in a potential reduction algorithm for linear programming. Mathematical Programming 59, 133–150 (1993). https://doi.org/10.1007/BF01581241

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  • DOI: https://doi.org/10.1007/BF01581241

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