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An implementation of a parallel primal-dual interior point method for block-structured linear programs

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Abstract

An implementation of the primal-dual predictor-corrector interior point method is specialized to solve block-structured linear programs with side constraints. The block structure of the constraint matrix is exploited via parallel computation. The side constraints require the Cholesky factorization of a dense matrix, where a method that exploits parallelism for the dense Cholesky factorization is used. For testing, multicommodity flow problems were used. The resulting implementation is 65%–90% efficient, depending on the problem instance. For a problem with K commodities, an approximate speedup for the interior point method of 0.8K is realized.

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Authors and Affiliations

  1. Department of Civil Engineering and Operations Research, Princeton University, 08544, Princeton, NJ, USA

    Irvin J. Lustig

  2. Department of Mathematical Sciences, Rice University, 77251, Houston, TX, USA

    Guangye Li

  3. Center for Research in Parallel Computation, Rice University, 77251, Houston, TX, USA

    Guangye Li

Authors
  1. Irvin J. Lustig
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  2. Guangye Li
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Lustig, I.J., Li, G. An implementation of a parallel primal-dual interior point method for block-structured linear programs. Comput Optim Applic 1, 141–161 (1992). https://doi.org/10.1007/BF00253804

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  • DOI: https://doi.org/10.1007/BF00253804

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