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On the complex fractional quadratic optimization with a quadratic constraint

Author

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  • S. Fallahi

    (Salman Farsi University of Kazerun)

  • M. Salahi

    (University of Guilan)

Abstract

In this paper, we study the problem of minimizing the ratio of two complex indefinite quadratic functions subject to a strictly convex quadratic constraint. First, using the known method due to Dinkelbach, we reformulate the fractional problem as a univariate equation. To find the root of the univariate equation, the generalized Newton method is utilized that requires solving a nonconvex quadratic optimization problem at each iteration. To solve these nonconvex quadratic problems, we present an efficient algorithm by a diagonalization scheme that requires solving a univariate minimization problem at each iteration. Moreover, for the homogeneous case, it requires solving a simple linear optimization problem. Our preliminary numerical experiments on several randomly generated test problems show that, the new approach is much faster in finding the global optimal solution than the known semidefinite relaxation approach, especially when solving large scale problems.

Suggested Citation

  • S. Fallahi & M. Salahi, 2017. "On the complex fractional quadratic optimization with a quadratic constraint," OPSEARCH, Springer;Operational Research Society of India, vol. 54(1), pages 94-106, March.
    • Handle: RePEc:spr:opsear:v:54:y:2017:i:1:d:10.1007_s12597-016-0263-8
    DOI: 10.1007/s12597-016-0263-8
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    References listed on IDEAS

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    1. Yongwei Huang & Shuzhong Zhang, 2007. "Complex Matrix Decomposition and Quadratic Programming," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 758-768, August.
    2. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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    Cited by:

    1. Vandana Goyal & Namrata Rani & Deepak Gupta, 2022. "FGP approach to quadratically constrained multi-objective quadratic fractional programming with parametric functions," OPSEARCH, Springer;Operational Research Society of India, vol. 59(2), pages 594-602, June.

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