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A study of the difference-of-convex approach for solving linear programs with complementarity constraints

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Abstract

This paper studies the difference-of-convex (DC) penalty formulations and the associated difference-of-convex algorithm (DCA) for computing stationary solutions of linear programs with complementarity constraints (LPCCs). We focus on three such formulations and establish connections between their stationary solutions and those of the LPCC. Improvements of the DCA are proposed to remedy some drawbacks in a straightforward adaptation of the DCA to these formulations. Extensive numerical results, including comparisons with an existing nonlinear programming solver and the mixed-integer formulation, are presented to elucidate the effectiveness of the overall DC approach.

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Acknowledgements

We thank a referee for very helpful comments that have improved the presentation of the paper.

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Correspondence to Andreas Wächter.

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The first and third author were supported in part by the U.S. National Science Foundation Grant CMMI-1334639. The second author was partially supported by the U.S. National Science Foundation Grant CMMI-1402052 and the Air Force Office of Sponsored Research Grant FA9550-15-1-0126.

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Jara-Moroni, F., Pang, JS. & Wächter, A. A study of the difference-of-convex approach for solving linear programs with complementarity constraints. Math. Program. 169, 221–254 (2018). https://doi.org/10.1007/s10107-017-1208-6

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  • DOI: https://doi.org/10.1007/s10107-017-1208-6

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