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Global minimization of indefinite quadratic functions subject to box constraints

Author

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  • Pierre Hansen
  • Brigitte Jaumard
  • MichèLe Ruiz
  • Junjie Xiong

Abstract

A branch‐and‐bound algorithm is proposed for global minimization of indefinite quadratic functions subject to box constraints. Branching is done according to the sign of first‐order derivatives. New tests based on the compatibility of signs of several first‐order derivatives and on various bounding procedures, allow curtailment of the search. Computational experiments are reported. Comparison is made with an interval arithmetic implementation. © 1993 John Wiley & Sons, Inc.

Suggested Citation

  • Pierre Hansen & Brigitte Jaumard & MichèLe Ruiz & Junjie Xiong, 1993. "Global minimization of indefinite quadratic functions subject to box constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(3), pages 373-392, April.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:3:p:373-392
    DOI: 10.1002/1520-6750(199304)40:33.0.CO;2-A
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    References listed on IDEAS

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    1. Paul F. Kough, 1979. "The Indefinite Quadratic Programming Problem," Operations Research, INFORMS, vol. 27(3), pages 516-533, June.
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    Cited by:

    1. Benjamin Beach & Robert Hildebrand & Joey Huchette, 2022. "Compact mixed-integer programming formulations in quadratic optimization," Journal of Global Optimization, Springer, vol. 84(4), pages 869-912, December.
    2. Samuel Burer & Dieter Vandenbussche, 2009. "Globally solving box-constrained nonconvex quadratic programs with semidefinite-based finite branch-and-bound," Computational Optimization and Applications, Springer, vol. 43(2), pages 181-195, June.
    3. Riccardo Cambini & Claudio Sodini, 2008. "A computational comparison of some branch and bound methods for indefinite quadratic programs," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 139-152, June.
    4. Yash Puranik & Nikolaos V. Sahinidis, 2017. "Bounds tightening based on optimality conditions for nonconvex box-constrained optimization," Journal of Global Optimization, Springer, vol. 67(1), pages 59-77, January.
    5. Wei Xia & Juan C. Vera & Luis F. Zuluaga, 2020. "Globally Solving Nonconvex Quadratic Programs via Linear Integer Programming Techniques," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 40-56, January.

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