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Relaxations and cutting planes for linear programs with complementarity constraints

Author

Listed:
  • Alberto Pia

    (University of Wisconsin-Madison)

  • Jeff Linderoth

    (University of Wisconsin-Madison)

  • Haoran Zhu

    (University of Wisconsin-Madison)

Abstract

We study relaxations for linear programs with complementarity constraints, especially instances whose complementary pairs of variables are not independent. Our formulation is based on identifying vertex covers of the conflict graph of the instance and contains the extended formulation obtained from the ERLT introduced by Nguyen, Richard, and Tawarmalani as a special case. We demonstrate how to obtain strong cutting planes for our formulation from both the stable set polytope and the boolean quadric polytope associated with a complete bipartite graph. Through an extensive computational study for three types of practical problems, we assess the performance of our proposed linear relaxation and new cutting-planes in terms of the optimality gap closed.

Suggested Citation

  • Alberto Pia & Jeff Linderoth & Haoran Zhu, 2024. "Relaxations and cutting planes for linear programs with complementarity constraints," Journal of Global Optimization, Springer, vol. 90(1), pages 27-51, September.
    • Handle: RePEc:spr:jglopt:v:90:y:2024:i:1:d:10.1007_s10898-024-01397-x
    DOI: 10.1007/s10898-024-01397-x
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