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

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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.

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Acknowledgements

The author would like to thank Prof. Jen-Chih Yao and Prof. Hsien-Chung Wu for helping him to thoroughly check the original manuscript and providing the valuable comments which definitely improve the presentation of this paper. Research is partially supported by NSC 100-2115-M-037-001.

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  1. Center for General Education Kaohsiung Medical University, Kaohsiung, 807, Taiwan

    Ching-Feng Wen

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  1. Ching-Feng Wen
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Correspondence to Ching-Feng Wen.

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Communicated by Jen-Chih Yao.

This paper is dedicated to the memory of my father Ho-Tsung Wen.

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Wen, CF. Continuous-Time Generalized Fractional Programming Problems. Part I: Basic Theory. J Optim Theory Appl 157, 365–399 (2013). https://doi.org/10.1007/s10957-012-0163-x

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