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Generating Sum-of-Ratios Test Problems in Global Optimization

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  • H. P. Benson

    (University of Florida)

Abstract

A method is presented for the construction of test problems involving the minimization over convex sets of sums of ratios of affine functions. Given a nonempty, compact convex set, the method determines a function that is the sum of linear fractional functions and attains a global minimum over the set at a point that can be found by convex programming and univariate search. Generally, the function will have also local minima over the set that are not global minima.

Suggested Citation

  • H. P. Benson, 2003. "Generating Sum-of-Ratios Test Problems in Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 119(3), pages 615-621, December.
    • Handle: RePEc:spr:joptap:v:119:y:2003:i:3:d:10.1023_b:jota.0000006959.01650.59
    DOI: 10.1023/B:JOTA.0000006959.01650.59
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    Cited by:

    1. Laura Carosi & Laura Martein, 2008. "A sequential method for a class of pseudoconcave fractional problems," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 16(2), pages 153-164, June.
    2. Laura Carosi & Laura Martein & Ezat Valipour, 2013. "Simplex-like sequential methods for a class of generalized fractional programs," Discussion Papers 2013/168, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    3. 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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