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Unconstrained formulation of standard quadratic optimization problems

Author

Listed:
  • 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)

Abstract
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.

Suggested Citation

  • 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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    File URL: http://www.dis.uniroma1.it/~bibdis/RePEc/aeg/wpaper/2010-12.pdf
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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. Riccardo Bisori & Matteo Lapucci & Marco Sciandrone, 2022. "A study on sequential minimal optimization methods for standard quadratic problems," 4OR, Springer, vol. 20(4), pages 685-712, December.
    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. 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.
    5. Wang, Xing & Tao, Chang-qi & Tang, Guo-ji, 2015. "A class of differential quadratic programming problems," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 369-377.

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