Computational Optimization and Applications

, Volume 35, Issue 2, pp 135–159 | Cite as

Optimization of a Quadratic Function with a Circulant Matrix

  • Nguyen Thi Hoai Phuong
  • Hoang Tuy
  • Faiz Al-Khayyal


A problem arising in the control of flutter in compression systems via mistuning is formulated as maximizing a quadratic function with a circulant matrix over a set of vectors whose every component can take one of three values (the three level problem) or one of two values (the two level problem).


Mistuning problem quadratic optimization circulant matrix 


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  1. 1.
    F.A. Al-Khayyal and C. Larson, “Global minimization of a quadratic function subject to bounded mixed integer constraints,” Annals of Operations Research, vol. 25, pp. 169–180, 1990.zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    P.J. Davis, Circulant Matrices, Wiley & Sons 1979.Google Scholar
  3. 3.
    C.A. Floudas, Deterministic global optimization: Theory, methods and applications, Kluwer 2000.Google Scholar
  4. 4.
    P.M. Pardalos and G.P. Rodgers, “A branch and bound algorithm for the maximum clique problem,” Computers Ops. Res., vol. 19, pp. 363–375, 1992.zbMATHCrossRefGoogle Scholar
  5. 5.
    B. Shapiro, “Symmetry approach to extension of flutter boundaries via mistuning,” Journal of Propulsion and Power, vol. 14 no. 3, pp. 354–366, 1998.CrossRefGoogle Scholar
  6. 6.
    B. Shapiro, “Passive control of flutter and forced response in bladed disks via mistuning,” Ph. D. Dissertation, California Institute of Technology, Pasadena, CA, 1999.Google Scholar
  7. 7.
    H. D. Sherali and W. P. Adams, A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems, Kluwer 1999.Google Scholar
  8. 8.
    H. Tuy, in Convex Analysis and Global Optimization, Kluwer, 1998.Google Scholar
  9. 9.
    H. Tuy, “Monotonic optimization: problems and solution approaches,” SIAM Journal on Optimization, vol. 11 no. 2, pp. 464–494, 2000.zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    H. Tuy, M. Minoux and N.T. Hoai-Phuong, “Discrete monotonic optimization with application to a discrete location problem,” to appear in SIAM Journal on Optimization, 2006.Google Scholar
  11. 11.
    Fuzhen Zhang, Matrix Theory, Springer, 1999.Google Scholar

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  • Nguyen Thi Hoai Phuong
    • 1
  • Hoang Tuy
    • 1
  • Faiz Al-Khayyal
    • 2
  1. 1.Institute of MathematicsBo HoVietnam
  2. 2.School of Industrial Systems and EngineeringGeorgia Institute of TechnologyAtlantaUSA

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