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Sufficient Global Optimality Conditions for Bivalent Quadratic Optimization

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  • M. Ç. Pinar

    (Bilkent University)

Abstract

We prove a sufficient global optimality condition for the problem of minimizing a quadratic function subject to quadratic equality constraints where the variables are allowed to take values −1 and 1. We extend the condition to quadratic problems with matrix variables and orthonormality constraints, and in particular to the quadratic assignment problem.

Suggested Citation

  • M. Ç. Pinar, 2004. "Sufficient Global Optimality Conditions for Bivalent Quadratic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 433-440, August.
    • Handle: RePEc:spr:joptap:v:122:y:2004:i:2:d:10.1023_b:jota.0000042530.24671.80
    DOI: 10.1023/B:JOTA.0000042530.24671.80
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    Citations

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    Cited by:

    1. Wu, Zhiyou & Tian, Jing & Quan, Jing & Ugon, Julien, 2014. "Optimality conditions and optimization methods for quartic polynomial optimization," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 968-982.
    2. Amar Andjouh & Mohand Ouamer Bibi, 2022. "Adaptive Global Algorithm for Solving Box-Constrained Non-convex Quadratic Minimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 360-378, January.
    3. Guoyin Li, 2012. "Global Quadratic Minimization over Bivalent Constraints: Necessary and Sufficient Global Optimality Condition," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 710-726, March.
    4. V. Jeyakumar & G. Li & S. Srisatkunarajah, 2014. "Global optimality principles for polynomial optimization over box or bivalent constraints by separable polynomial approximations," Journal of Global Optimization, Springer, vol. 58(1), pages 31-50, January.
    5. Thai Doan Chuong, 2020. "Semidefinite Program Duals for Separable Polynomial Programs Involving Box Constraints," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 289-299, April.
    6. Z. Y. Wu & V. Jeyakumar & A. M. Rubinov, 2007. "Sufficient Conditions for Global Optimality of Bivalent Nonconvex Quadratic Programs with Inequality Constraints," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 123-130, April.
    7. Gary Kochenberger & Jin-Kao Hao & Fred Glover & Mark Lewis & Zhipeng Lü & Haibo Wang & Yang Wang, 2014. "The unconstrained binary quadratic programming problem: a survey," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 58-81, July.
    8. Z. Y. Wu & Y. J. Yang & F. S. Bai & M. Mammadov, 2011. "Global Optimality Conditions and Optimization Methods for Quadratic Knapsack Problems," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 241-259, November.
    9. Z. Y. Wu & A. M. Rubinov, 2010. "Global Optimality Conditions for Some Classes of Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 164-185, April.
    10. Xue-Gang Zhou & Xiao-Peng Yang & Bing-Yuan Cao, 2015. "Global optimality conditions for cubic minimization problems with cubic constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(3), pages 243-264, December.
    11. X. Zheng & X. Sun & D. Li & Y. Xu, 2012. "On zero duality gap in nonconvex quadratic programming problems," Journal of Global Optimization, Springer, vol. 52(2), pages 229-242, February.
    12. Hossein Mohebi & Alexander Rubinov, 2006. "Metric Projection onto a Closed Set: Necessary and Sufficient Conditions for the Global Minimum," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 124-132, February.

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