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Unconstrained formulation of standard quadratic optimization problems

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  • Immanuel Bomze
  • Luigi Grippo
  • Laura Palagi

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.
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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. 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.
    2. 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.
    3. 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.
    4. 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.
    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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