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Global solutions to fractional programming problem with ratio of nonconvex functions

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  • Ruan, N.
  • Gao, D.Y.

Abstract

This paper presents a canonical dual approach for minimizing a sum of quadratic function and a ratio of nonconvex functions in Rn. By introducing a parameter, the problem is first equivalently reformed as a nonconvex polynomial minimization with elliptic constraint. It is proved that under certain conditions, the canonical dual is a concave maximization problem in R2 that exhibits no duality gap. Therefore, the global optimal solution of the primal problem can be obtained by solving the canonical dual problem.

Suggested Citation

  • Ruan, N. & Gao, D.Y., 2015. "Global solutions to fractional programming problem with ratio of nonconvex functions," Applied Mathematics and Computation, Elsevier, vol. 255(C), pages 66-72.
    • Handle: RePEc:eee:apmaco:v:255:y:2015:i:c:p:66-72
    DOI: 10.1016/j.amc.2014.08.060
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    References listed on IDEAS

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    1. C. H. Scott & T. R. Jefferson, 1998. "Duality of a Nonconvex Sum of Ratios," Journal of Optimization Theory and Applications, Springer, vol. 98(1), pages 151-159, July.
    2. Y. Almogy & O. Levin, 1971. "A Class of Fractional Programming Problems," Operations Research, INFORMS, vol. 19(1), pages 57-67, February.
    3. 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.
    4. H. P. Benson, 2004. "On the Global Optimization of Sums of Linear Fractional Functions over a Convex Set," Journal of Optimization Theory and Applications, Springer, vol. 121(1), pages 19-39, April.
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