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Fractional Programming. II, On Dinkelbach's Algorithm

Author

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  • Siegfried Schaible

    (University of Cologne and Stanford University)

Abstract

Dinkelbach's algorithm [Dinkelbach, W. 1967. On nonlinear fractional programming. Management Sci. 13 492-498.] solving the parametric equivalent of a fractional program is investigated. It is shown that the algorithm converges superlinearly and often (locally) quadratically. A priori and a posteriori error estimates are derived. Using those estimates and duality as introduced in Part I, a revised version of the algorithm is proposed. In addition, a similar algorithm is presented where, in contrast to Dinkelbach's procedure, the rate of convergence is still controllable. Error estimates are derived also for this algorithm.

Suggested Citation

  • Siegfried Schaible, 1976. "Fractional Programming. II, On Dinkelbach's Algorithm," Management Science, INFORMS, vol. 22(8), pages 868-873, April.
    • Handle: RePEc:inm:ormnsc:v:22:y:1976:i:8:p:868-873
    DOI: 10.1287/mnsc.22.8.868
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    Cited by:

    1. Wong, Man Hong, 2013. "Investment models based on clustered scenario trees," European Journal of Operational Research, Elsevier, vol. 227(2), pages 314-324.
    2. Garrido, Rodrigo A. & Bronfman, Andrés C., 2017. "Equity and social acceptability in multiple hazardous materials routing through urban areas," Transportation Research Part A: Policy and Practice, Elsevier, vol. 102(C), pages 244-260.
    3. Joaquim Júdice & Valentina Sessa & Masao Fukushima, 2022. "Solution of Fractional Quadratic Programs on the Simplex and Application to the Eigenvalue Complementarity Problem," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 545-573, June.
    4. R. Yamamoto & H. Konno, 2007. "An Efficient Algorithm for Solving Convex–Convex Quadratic Fractional Programs," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 241-255, May.
    5. Paula Alexandra Amaral & Immanuel M. Bomze, 2019. "Nonconvex min–max fractional quadratic problems under quadratic constraints: copositive relaxations," Journal of Global Optimization, Springer, vol. 75(2), pages 227-245, October.
    6. Xiang-Kai Sun & Xian-Jun Long & Yi Chai, 2015. "Sequential Optimality Conditions for Fractional Optimization with Applications to Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 479-499, February.
    7. Frauke Liers & Lars Schewe & Johannes Thürauf, 2022. "Radius of Robust Feasibility for Mixed-Integer Problems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 243-261, January.
    8. 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.
    9. Juan S. Borrero & Colin Gillen & Oleg A. Prokopyev, 2017. "Fractional 0–1 programming: applications and algorithms," Journal of Global Optimization, Springer, vol. 69(1), pages 255-282, September.
    10. Bram L. Gorissen, 2015. "Robust Fractional Programming," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 508-528, August.
    11. T Peña & P Lara & C Castrodeza, 2009. "Multiobjective stochastic programming for feed formulation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1738-1748, December.
    12. Cook, Wade D. & Zhu, Joe, 2007. "Within-group common weights in DEA: An analysis of power plant efficiency," European Journal of Operational Research, Elsevier, vol. 178(1), pages 207-216, April.

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