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Optimization of a Quadratic Function with a Circulant Matrix

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Abstract

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).

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References

  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.

    Article  MATH  MathSciNet  Google Scholar 

  2. P.J. Davis, Circulant Matrices, Wiley & Sons 1979.

  3. C.A. Floudas, Deterministic global optimization: Theory, methods and applications, Kluwer 2000.

  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.

    Article  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  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.

  7. H. D. Sherali and W. P. Adams, A Reformulation-Linearization Technique for Solving Discrete and Continuous Nonconvex Problems, Kluwer 1999.

  8. H. Tuy, in Convex Analysis and Global Optimization, Kluwer, 1998.

  9. H. Tuy, “Monotonic optimization: problems and solution approaches,” SIAM Journal on Optimization, vol. 11 no. 2, pp. 464–494, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  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.

  11. Fuzhen Zhang, Matrix Theory, Springer, 1999.

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Authors and Affiliations

  1. Institute of Mathematics, P.O. Box 631, Bo Ho, Hanoi, Vietnam

    Nguyen Thi Hoai Phuong & Hoang Tuy

  2. School of Industrial Systems and Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0205, USA

    Faiz Al-Khayyal

Authors
  1. Nguyen Thi Hoai Phuong
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  2. Hoang Tuy
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  3. Faiz Al-Khayyal
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Phuong, N.T.H., Tuy, H. & Al-Khayyal, F. Optimization of a Quadratic Function with a Circulant Matrix. Comput Optim Applic 35, 135–159 (2006). https://doi.org/10.1007/s10589-006-6448-y

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  • DOI: https://doi.org/10.1007/s10589-006-6448-y

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