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Using the parametric approach to solve the continuous-time linear fractional max–min problems

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  • Ching-Feng Wen

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  • Hsien-Chung Wu

    ()

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    Abstract

    A numerical algorithm based on parametric approach is proposed in this paper to solve a class of continuous-time linear fractional max-min programming problems. We shall transform this original problem into a continuous-time non-fractional programming problem, which unfortunately happens to be a continuous-time nonlinear programming problem. In order to tackle this nonlinear problem, we propose the auxiliary problem that will be formulated as a parametric continuous-time linear programming problem. We also introduce a dual problem of this parametric continuous-time linear programming problem in which the weak duality theorem also holds true. We introduce the discrete approximation method to solve the primal and dual pair of parametric continuous-time linear programming problems by using the recurrence method. Finally, we provide two numerical examples to demonstrate the usefulness of this algorithm. Copyright Springer Science+Business Media, LLC. 2012

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    File URL: http://hdl.handle.net/10.1007/s10898-011-9751-9
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    Bibliographic Info

    Article provided by Springer in its journal Journal of Global Optimization.

    Volume (Year): 54 (2012)
    Issue (Month): 1 (September)
    Pages: 129-153

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    Handle: RePEc:spr:jglopt:v:54:y:2012:i:1:p:129-153

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    Web page: http://www.springer.com/business/operations+research/journal/10898

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    Related research

    Keywords: Approximate solutions; Continuous-time linear fractional max-min programming problems; Weak duality;

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    1. Schaible, Siegfried & Ibaraki, Toshidide, 1983. "Fractional programming," European Journal of Operational Research, Elsevier, vol. 12(4), pages 325-338, April.
    2. Ching-Feng Wen & Hsien-Chung Wu, 2011. "Using the Dinkelbach-type algorithm to solve the continuous-time linear fractional programming problems," Journal of Global Optimization, Springer, vol. 49(2), pages 237-263, February.
    3. Schaible, Siegfried, 1981. "Fractional programming: Applications and algorithms," European Journal of Operational Research, Elsevier, vol. 7(2), pages 111-120, June.
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