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Solving combinatorial optimization problems using Karmarkar's algorithm

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Abstract

We describe a cutting plane algorithm for solving combinatorial optimization problems. The primal projective standard-form variant of Karmarkar's algorithm for linear programming is applied to the duals of a sequence of linear programming relaxations of the combinatorial optimization problem.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 12180, Troy, NY, USA

    John E. Mitchell

  2. School of Operations Research and Industrial Engineering, Cornell University, 14853, Ithaca, NY, USA

    Michael J. Todd

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  1. John E. Mitchell
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  2. Michael J. Todd
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Additional information

Computational facilities provided by the Cornell Computational Optimization Project supported by NSF Grant DMS-8706133 and by the Cornell National Supercomputer Facility. The Cornell National Supercomputer Facility is a resource of the Center for Theory and Simulation in Science and Engineering at Cornell Unversity, which is funded in part by the National Science Foundation, New York State, and the IBM Corporation. The research of both authors was partially supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University.

Research partially supported by ONR Grant N00014-90-J-1714.

Research partially supported by NSF Grant ECS-8602534 and by ONR Contract N00014-87-K-0212.

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Mitchell, J.E., Todd, M.J. Solving combinatorial optimization problems using Karmarkar's algorithm. Mathematical Programming 56, 245–284 (1992). https://doi.org/10.1007/BF01580902

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  • DOI: https://doi.org/10.1007/BF01580902

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