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Efficient local search procedures for quadratic fractional programming problems

Author

Listed:
  • Luca Consolini

    (Università di Parma)

  • Marco Locatelli

    (Università di Parma)

  • Jiulin Wang

    (Beihang University)

  • Yong Xia

    (Beihang University)

Abstract

The problem of minimizing the sum of a convex quadratic function and the ratio of two quadratic functions can be reformulated as a Celis–Dennis–Tapia (CDT) problem and, thus, according to some recent results, can be polynomially solved. However, the degree of the known polynomial approaches for these problems is fairly large and that justifies the search for efficient local search procedures. In this paper the CDT reformulation of the problem is exploited to define a local search algorithm. On the theoretical side, its convergence to a stationary point is proved. On the practical side it is shown, through different numerical experiments, that the main cost of the algorithm is a single Schur decomposition to be performed during the initialization phase. The theoretical and practical results for this algorithm are further strengthened in a special case.

Suggested Citation

  • Luca Consolini & Marco Locatelli & Jiulin Wang & Yong Xia, 2020. "Efficient local search procedures for quadratic fractional programming problems," Computational Optimization and Applications, Springer, vol. 76(1), pages 201-232, May.
    • Handle: RePEc:spr:coopap:v:76:y:2020:i:1:d:10.1007_s10589-020-00175-1
    DOI: 10.1007/s10589-020-00175-1
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    References listed on IDEAS

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    1. H. P. Benson, 2007. "Solving Sum of Ratios Fractional Programs via Concave Minimization," Journal of Optimization Theory and Applications, Springer, vol. 135(1), pages 1-17, October.
    2. H. P. Benson, 2002. "Global Optimization Algorithm for the Nonlinear Sum of Ratios Problem," Journal of Optimization Theory and Applications, Springer, vol. 112(1), pages 1-29, January.
    3. Meijia Yang & Yong Xia & Jiulin Wang & Jiming Peng, 2018. "Efficiently solving total least squares with Tikhonov identical regularization," Computational Optimization and Applications, Springer, vol. 70(2), pages 571-592, June.
    4. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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