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Unconstrained formulation of standard quadratic optimization problems


  • Immanuel Bomze


  • Luigi Grippo
  • Laura Palagi


A standard quadratic optimization problem (StQP) consists of nding the largest or smallest value of a (possibly indenite) quadratic form over the standard simplex which is the intersection of a hyperplane with the positive orthant. This NP-hard problem has several immediate real-world applications like the Maximum-Clique Problem, and it also occurs in a natural way as a subproblem in quadratic programming with linear constraints. We propose unconstrained reformulations of StQPs, by using dierent approaches. We test our method on clique problems from the DIMACS challenge.
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Suggested Citation

  • Immanuel Bomze & Luigi Grippo & Laura Palagi, 2012. "Unconstrained formulation of standard quadratic optimization problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 35-51, April.
  • Handle: RePEc:spr:topjnl:v:20:y:2012:i:1:p:35-51
    DOI: 10.1007/s11750-010-0166-4

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    Cited by:

    1. Immanuel Bomze & Chen Ling & Liqun Qi & Xinzhen Zhang, 2012. "Standard bi-quadratic optimization problems and unconstrained polynomial reformulations," Journal of Global Optimization, Springer, vol. 52(4), pages 663-687, April.
    2. Dellepiane, Umberto & Palagi, Laura, 2015. "Using SVM to combine global heuristics for the Standard Quadratic Problem," European Journal of Operational Research, Elsevier, vol. 241(3), pages 596-605.
    3. Tatyana Gruzdeva, 2013. "On a continuous approach for the maximum weighted clique problem," Journal of Global Optimization, Springer, vol. 56(3), pages 971-981, July.
    4. repec:eee:apmaco:v:270:y:2015:i:c:p:369-377 is not listed on IDEAS


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