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Branch-and-cut for complementarity-constrained optimization

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We report and analyze the results of our computational testing of branch-and-cut for the complementarity-constrained optimization problem (CCOP). Besides the MIP cuts commonly present in commercial optimization software, we used inequalities that explore complementarity constraints. To do so, we generalized two families of cuts proposed earlier by de Farias, Johnson, and Nemhauser that had never been tested computationally. Our test problems consisted of linear, binary, and general integer programs with complementarity constraints. Our results on the use of complementarity cuts within a major commercial optimization solver show that they are of critical importance to tackling difficult CCOP instances, typically reducing the computational time required to solve them tremendously.

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Acknowledgments

The authors acknowledge the High Performance Computing Center at Texas Tech University at Lubbock for providing resources that have contributed to the research results reported within this paper. URL: http://www.hpcc.ttu.edu. This research was partially supported by the Office of Naval Research (ONR) through grants N000140910332 and N000141310041. ONR’s support is gratefully acknowledged.

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Authors and Affiliations

  1. Texas Tech, Lubbock, USA

    I. R. de Farias Jr. & E. Kozyreff

  2. SAS, Cary, USA

    M. Zhao

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  1. I. R. de Farias Jr.
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  2. E. Kozyreff
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  3. M. Zhao
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Correspondence to I. R. de Farias Jr..

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de Farias, I.R., Kozyreff, E. & Zhao, M. Branch-and-cut for complementarity-constrained optimization. Math. Prog. Comp. 6, 365–403 (2014). https://doi.org/10.1007/s12532-014-0070-2

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  • DOI: https://doi.org/10.1007/s12532-014-0070-2

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