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Converging upon basic feasible solutions through Dantzig–Wolfe decomposition

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Abstract

We derive an important property for solving large-scale integer programs by examining the master problem in Dantzig–Wolfe decomposition. In particular, we prove that if a linear program can be divided into subproblems with affinely independent corner points, then there is a direct mapping between basic feasible solutions in the master and original problems. This has implications for integer programs where the feasible region has integer corner points, ensuring that integer solutions to the original problem will be found even through the decomposition approach. An application to air traffic flow scheduling, which motivated this result, is highlighted.

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Authors and Affiliations

  1. NASA Ames Research Center, MS 210-15, Moffett Field, CA, 94035, USA

    Joseph L. Rios

  2. School of Engineering, University of California at Santa Cruz, Santa Cruz, CA, 95064, USA

    Kevin Ross

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  1. Joseph L. Rios
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  2. Kevin Ross
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Correspondence to Joseph L. Rios.

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Rios, J.L., Ross, K. Converging upon basic feasible solutions through Dantzig–Wolfe decomposition. Optim Lett 8, 171–180 (2014). https://doi.org/10.1007/s11590-012-0546-9

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  • DOI: https://doi.org/10.1007/s11590-012-0546-9

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