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A Lagrangian relaxation approach to the edge-weighted clique problem

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  • Hunting, Marcel
  • Faigle, Ulrich
  • Kern, Walter

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  • Hunting, Marcel & Faigle, Ulrich & Kern, Walter, 2001. "A Lagrangian relaxation approach to the edge-weighted clique problem," European Journal of Operational Research, Elsevier, vol. 131(1), pages 119-131, May.
    • Handle: RePEc:eee:ejores:v:131:y:2001:i:1:p:119-131
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    References listed on IDEAS

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    1. Macambira, Elder Magalhaes & de Souza, Cid Carvalho, 2000. "The edge-weighted clique problem: Valid inequalities, facets and polyhedral computations," European Journal of Operational Research, Elsevier, vol. 123(2), pages 346-371, June.
    2. Endre Boros & Peter L. Hammer, 1993. "Cut-Polytopes, Boolean Quadric Polytopes and Nonnegative Quadratic Pseudo-Boolean Functions," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 245-253, February.
    3. Kurt M. Bretthauer & Bala Shetty & Siddhartha Syam, 1995. "A Branch and Bound Algorithm for Integer Quadratic Knapsack Problems," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 109-116, February.
    4. Dijkhuizen, G. & Faigle, U., 1993. "A cutting-plane approach to the edge-weighted maximal clique problem," European Journal of Operational Research, Elsevier, vol. 69(1), pages 121-130, August.
    5. Park, Kyungchul & Lee, Kyungsik & Park, Sungsoo, 1996. "An extended formulation approach to the edge-weighted maximal clique problem," European Journal of Operational Research, Elsevier, vol. 95(3), pages 671-682, December.
    6. S. S. Ravi & D. J. Rosenkrantz & G. K. Tayi, 1994. "Heuristic and Special Case Algorithms for Dispersion Problems," Operations Research, INFORMS, vol. 42(2), pages 299-310, April.
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    Cited by:

    1. Jayaraman, Vaidyanathan & Gupta, Rakesh & Pirkul, Hasan, 2003. "Selecting hierarchical facilities in a service-operations environment," European Journal of Operational Research, Elsevier, vol. 147(3), pages 613-628, June.
    2. Seyedmohammadhossein Hosseinian & Dalila B. M. M. Fontes & Sergiy Butenko, 2020. "A Lagrangian Bound on the Clique Number and an Exact Algorithm for the Maximum Edge Weight Clique Problem," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 747-762, July.
    3. Seyedmohammadhossein Hosseinian & Dalila B. M. M. Fontes & Sergiy Butenko, 2018. "A nonconvex quadratic optimization approach to the maximum edge weight clique problem," Journal of Global Optimization, Springer, vol. 72(2), pages 219-240, October.
    4. Michael M. Sørensen, 2004. "b-Tree Facets for the Simple Graph Partitioning Polytope," Journal of Combinatorial Optimization, Springer, vol. 8(2), pages 151-170, June.
    5. Abilio Lucena, 2005. "Non Delayed Relax-and-Cut Algorithms," Annals of Operations Research, Springer, vol. 140(1), pages 375-410, November.
    6. Alidaee, Bahram & Glover, Fred & Kochenberger, Gary & Wang, Haibo, 2007. "Solving the maximum edge weight clique problem via unconstrained quadratic programming," European Journal of Operational Research, Elsevier, vol. 181(2), pages 592-597, September.
    7. Martinhon, Carlos & Lucena, Abilio & Maculan, Nelson, 2004. "Stronger K-tree relaxations for the vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 158(1), pages 56-71, October.
    8. Sorensen, Michael M., 2004. "New facets and a branch-and-cut algorithm for the weighted clique problem," European Journal of Operational Research, Elsevier, vol. 154(1), pages 57-70, April.
    9. Lourenco, Lidia Lampreia & Pato, Margarida Vaz, 2007. "The effect of strengthened linear formulations on improving the lower bounds for the part families with precedence constraints problem," European Journal of Operational Research, Elsevier, vol. 183(1), pages 181-196, November.
    10. Borgwardt, S. & Schmiedl, F., 2014. "Threshold-based preprocessing for approximating the weighted dense k-subgraph problem," European Journal of Operational Research, Elsevier, vol. 234(3), pages 631-640.
    11. San Segundo, Pablo & Coniglio, Stefano & Furini, Fabio & Ljubić, Ivana, 2019. "A new branch-and-bound algorithm for the maximum edge-weighted clique problem," European Journal of Operational Research, Elsevier, vol. 278(1), pages 76-90.

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