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Exploiting Group Symmetry in Semidefinite Programming Relaxations of the Quadratic Assignment Problem

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  • de Klerk, E.

    (Tilburg University, Center For Economic Research)

  • Sotirov, R.

    (Tilburg University, Center For Economic Research)

Abstract

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Suggested Citation

  • de Klerk, E. & Sotirov, R., 2007. "Exploiting Group Symmetry in Semidefinite Programming Relaxations of the Quadratic Assignment Problem," Discussion Paper 2007-44, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:87a5d126-86e5-4863-8ea5-1a76fc5f25e7
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    References listed on IDEAS

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    1. Ivanov, I.D. & de Klerk, E., 2007. "Parallel Implementation of a Semidefinite Programming Solver based on CSDP in a distributed memory cluster," Other publications TiSEM 9b41ff5e-2808-4d12-a58c-0, Tilburg University, School of Economics and Management.
    2. de Klerk, E. & Maharry, J. & Pasechnik, D.V. & Richter, B. & Salazar, G., 2006. "Improved bounds for the crossing numbers of Km,n and Kn," Other publications TiSEM eca87811-247d-489f-89c2-c, Tilburg University, School of Economics and Management.
    3. Qing Zhao & Stefan E. Karisch & Franz Rendl & Henry Wolkowicz, 1998. "Semidefinite Programming Relaxations for the Quadratic Assignment Problem," Journal of Combinatorial Optimization, Springer, vol. 2(1), pages 71-109, March.
    4. de Klerk, E. & Pasechnik, D.V. & Schrijver, A., 2007. "Reduction of symmetric semidefinite programs using the regular*-representation," Other publications TiSEM e418158e-b9dd-4372-b84c-e, Tilburg University, School of Economics and Management.
    5. Rendl, F. & Sotirov, R., 2007. "Bounds for the quadratic assignment problem using the bundle method," Other publications TiSEM b6d298bc-77c9-4a6d-a043-5, Tilburg University, School of Economics and Management.
    6. Ivanov, I.D. & de Klerk, E., 2007. "Parallel Implementation of a Semidefinite Programming Solver based on CSDP in a distributed memory cluster," Discussion Paper 2007-20, Tilburg University, Center for Economic Research.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Hu, Hao & Sotirov, Renata & Wolkowicz, Henry, 2023. "Facial reduction for symmetry reduced semidefinite and doubly nonnegative programs," Other publications TiSEM 8dd3dbae-58fd-4238-b786-e, Tilburg University, School of Economics and Management.
    2. José F. S. Bravo Ferreira & Yuehaw Khoo & Amit Singer, 2018. "Semidefinite programming approach for the quadratic assignment problem with a sparse graph," Computational Optimization and Applications, Springer, vol. 69(3), pages 677-712, April.
    3. Samuel Burer & Sunyoung Kim & Masakazu Kojima, 2014. "Faster, but weaker, relaxations for quadratically constrained quadratic programs," Computational Optimization and Applications, Springer, vol. 59(1), pages 27-45, October.
    4. Feizollahi, Mohammad Javad & Feyzollahi, Hadi, 2015. "Robust quadratic assignment problem with budgeted uncertain flows," Operations Research Perspectives, Elsevier, vol. 2(C), pages 114-123.
    5. de Klerk, E. & Pasechnik, D.V. & Sotirov, R., 2007. "On Semidefinite Programming Relaxations of the Travelling Salesman Problem (Replaced by DP 2008-96)," Other publications TiSEM 12999d3d-956a-4660-9ae4-5, Tilburg University, School of Economics and Management.
    6. Samuel Burer & Kyungchan Park, 2024. "A Strengthened SDP Relaxation for Quadratic Optimization Over the Stiefel Manifold," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 320-339, July.
    7. E. de Klerk & R. Sotirov & U. Truetsch, 2015. "A New Semidefinite Programming Relaxation for the Quadratic Assignment Problem and Its Computational Perspectives," INFORMS Journal on Computing, INFORMS, vol. 27(2), pages 378-391, May.
    8. van Dam, E.R. & Sotirov, R., 2015. "On bounding the bandwidth of graphs with symmetry," Other publications TiSEM 180849f1-e7d3-44d9-8424-5, Tilburg University, School of Economics and Management.
    9. de Klerk, E. & Pasechnik, D.V. & Sotirov, R., 2008. "On Semidefinite Programming Relaxations of the Traveling Salesman Problem (revision of DP 2007-101)," Discussion Paper 2008-96, Tilburg University, Center for Economic Research.
    10. Laurent, M., 2009. "Sums of squares, moment matrices and optimization over polynomials," Other publications TiSEM 9fef820b-69d2-43f2-a501-e, Tilburg University, School of Economics and Management.
    11. de Klerk, Etienne & -Nagy, Marianna E. & Sotirov, Renata & Truetsch, Uwe, 2014. "Symmetry in RLT-type relaxations for the quadratic assignment and standard quadratic optimization problems," European Journal of Operational Research, Elsevier, vol. 233(3), pages 488-499.
    12. Jiming Peng & Tao Zhu & Hezhi Luo & Kim-Chuan Toh, 2015. "Semi-definite programming relaxation of quadratic assignment problems based on nonredundant matrix splitting," Computational Optimization and Applications, Springer, vol. 60(1), pages 171-198, January.
    13. Brosch, Daniel & de Klerk, Etienne, 2021. "Jordan symmetry reduction for conic optimization over the doubly nonnegative cone: Theory and software," Other publications TiSEM 283da78a-b42f-47b4-b2b7-2, Tilburg University, School of Economics and Management.
    14. Matteo Fischetti & Michele Monaci & Domenico Salvagnin, 2012. "Three Ideas for the Quadratic Assignment Problem," Operations Research, INFORMS, vol. 60(4), pages 954-964, August.
    15. Yichuan Ding & Dongdong Ge & Henry Wolkowicz, 2011. "On Equivalence of Semidefinite Relaxations for Quadratic Matrix Programming," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 88-104, February.
    16. Fanz Rendl & Renata Sotirov, 2018. "The min-cut and vertex separator problem," Computational Optimization and Applications, Springer, vol. 69(1), pages 159-187, January.
    17. E. R. van Dam & R. Sotirov, 2015. "On Bounding the Bandwidth of Graphs with Symmetry," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 75-88, February.
    18. Xiaolong Kuang & Bissan Ghaddar & Joe Naoum-Sawaya & Luis F. Zuluaga, 2019. "Alternative SDP and SOCP approximations for polynomial optimization," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(2), pages 153-175, June.
    19. Nyberg, Axel & Westerlund, Tapio, 2012. "A new exact discrete linear reformulation of the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 220(2), pages 314-319.

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