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A new algorithm for generalized fractional programs

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Abstract

A new dual problem for convex generalized fractional programs with no duality gap is presented and it is shown how this dual problem can be efficiently solved using a parametric approach. The resulting algorithm can be seen as “dual” to the Dinkelbach-type algorithm for generalized fractional programs since it approximates the optimal objective value of the dual (primal) problem from below. Convergence results for this algorithm are derived and an easy condition to achieve superlinear convergence is also established. Moreover, under some additional assumptions the algorithm also recovers at the same time an optimal solution of the primal problem. We also consider a variant of this new algorithm, based on scaling the “dual” parametric function. The numerical results, in case of quadratic-linear ratios and linear constraints, show that the performance of the new algorithm and its scaled version is superior to that of the Dinkelbach-type algorithms. From the computational results it also appears that contrary to the primal approach, the “dual” approach is less influenced by scaling.

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Authors and Affiliations

  1. D.E.I.O., Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1700, Lisboa, Portugal

    A. I. Barros

  2. Econometric Institute, Erasmus University, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands

    J. B. G. Frenk & S. Zhang

  3. University of California at Riverside, 92521, Riverside, CA, USA

    S. Schaible

Authors
  1. A. I. Barros
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  2. J. B. G. Frenk
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  3. S. Schaible
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  4. S. Zhang
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Additional information

This research was carried out at the Econometric Institute, Erasmus University, Rotterdam, the Netherlands and was supported by J.N.I.C.T. (Portugal) under contract BD/707/90-RM.

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Barros, A.I., Frenk, J.B.G., Schaible, S. et al. A new algorithm for generalized fractional programs. Mathematical Programming 72, 147–175 (1996). https://doi.org/10.1007/BF02592087

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  • DOI: https://doi.org/10.1007/BF02592087

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