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Continuous-Time Generalized Fractional Programming Problems. Part I: Basic Theory

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  • Ching-Feng Wen

    (Center for General Education Kaohsiung Medical University)

Abstract

This study, that will be presented as two parts, develops a computational approach to a class of continuous-time generalized fractional programming problems. The parametric method for finite-dimensional generalized fractional programming is extended to problems posed in function spaces. The developed method is a hybrid of the parametric method and discretization approach. In this paper (Part I), some properties of continuous-time optimization problems in parametric form pertaining to continuous-time generalized fractional programming problems are derived. These properties make it possible to develop a computational procedure for continuous-time generalized fractional programming problems. However, it is notoriously difficult to find the exact solutions of continuous-time optimization problems. In the accompanying paper (Part II), a further computational procedure with approximation will be proposed. This procedure will yield bounds on errors introduced by the numerical approximation. In addition, both the size of discretization and the precision of an approximation approach depend on predefined parameters.

Suggested Citation

  • Ching-Feng Wen, 2013. "Continuous-Time Generalized Fractional Programming Problems. Part I: Basic Theory," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 365-399, May.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:2:d:10.1007_s10957-012-0163-x
    DOI: 10.1007/s10957-012-0163-x
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    References listed on IDEAS

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    1. Ching-Feng Wen & Yung-Yih Lur & Yan-Kuen Wu, 2010. "A recurrence method for a special class of continuous time linear programming problems," Journal of Global Optimization, Springer, vol. 47(1), pages 83-106, May.
    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. Ching-Feng Wen & Hsien-Chung Wu, 2012. "Using the parametric approach to solve the continuous-time linear fractional max–min problems," Journal of Global Optimization, Springer, vol. 54(1), pages 129-153, September.
    4. Werner Dinkelbach, 1967. "On Nonlinear Fractional Programming," Management Science, INFORMS, vol. 13(7), pages 492-498, March.
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