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Unconstrained formulation of standard quadratic optimization problems


  • Immanuel M. Bomze

    (Universidad de Buenos Aires)

  • Luigi Grippo

    () (Dipartimento di Informatica e Sistemistica "Antonio Ruberti" Sapienza, Universita' di Roma)

  • Laura Palagi

    () (Dipartimento di Informatica e Sistemistica "Antonio Ruberti" Sapienza, Universita' di Roma)


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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  • Immanuel M. Bomze & Luigi Grippo & Laura Palagi, 2010. "Unconstrained formulation of standard quadratic optimization problems," DIS Technical Reports 2010-12, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
  • Handle: RePEc:aeg:wpaper:2010-12

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    References listed on IDEAS

    1. Robert M. Saltzman & Frederick S. Hillier, 1992. "A Heuristic Ceiling Point Algorithm for General Integer Linear Programming," Management Science, INFORMS, vol. 38(2), pages 263-283, February.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. repec:eee:apmaco:v:270:y:2015:i:c:p:369-377 is not listed on IDEAS

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