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Spectral bounds for unconstrained (-1,1)-quadratic optimization problems

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  • Ben-Ameur, Walid
  • Neto, José

Abstract

Given an unconstrained quadratic optimization problem in the following form:with , we present different methods for computing bounds on its optimal objective value. Some of the lower bounds introduced are shown to generally improve over the one given by a classical semidefinite relaxation. We report on theoretical results on these new bounds and provide preliminary computational experiments on small instances of the maximum cut problem illustrating their performance.

Suggested Citation

  • Ben-Ameur, Walid & Neto, José, 2010. "Spectral bounds for unconstrained (-1,1)-quadratic optimization problems," European Journal of Operational Research, Elsevier, vol. 207(1), pages 15-24, November.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:1:p:15-24
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    References listed on IDEAS

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    1. Eranda Çela & Bettina Klinz & Christophe Meyer, 2006. "Polynomially solvable cases of the constant rank unconstrained quadratic 0-1 programming problem," Journal of Combinatorial Optimization, Springer, vol. 12(3), pages 187-215, November.
    2. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    3. Francisco Barahona & Martin Grötschel & Michael Jünger & Gerhard Reinelt, 1988. "An Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design," Operations Research, INFORMS, vol. 36(3), pages 493-513, June.
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