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

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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.

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Authors and Affiliations

  1. Center for General Education, Kaohsiung Medical University, Kaohsiung, 802, Taiwan

    Ching-Feng Wen

  2. Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, 802, Taiwan

    Hsien-Chung Wu

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  1. Ching-Feng Wen
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  2. Hsien-Chung Wu
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Correspondence to Hsien-Chung Wu.

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Wen, CF., Wu, HC. Using the parametric approach to solve the continuous-time linear fractional max–min problems. J Glob Optim 54, 129–153 (2012). https://doi.org/10.1007/s10898-011-9751-9

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