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Norm–based approximation in E-[0,1] convex multi-objective programming

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Abstract

This paper addresses the problem of capturing nondominated points on non-convex pareto frontier, which are encountered in E-[0,1] convex multi-objective programming problems. We use E-[0,1] map to transfer non-convex pareto frontier to convex pareto frontier, then An algorithm to find a piecewise linear approximation of the nondominated set of convex pareto frontier are applied. Finally, the inverse map of E-[0,1] is used to get the nondominated set of non-convex pareto frontier.

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Acknowledgments

We are grateful to everyone, who contributed, in one way or another, to the successful achievement of this paper for their help during the course of this work. Also, we would like to thank UoH to support us.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Hail, Ha’il, Kingdom of Saudi Arabia

    Tarek Emam & S. I. Ali

  2. Department of Mathematics, Faculty of Science, Suez University, Suez, Egypt

    Tarek Emam

  3. Mathematics Department, Faculty of Science, Al-Azher University, Cairo, Egypt

    S. I. Ali

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  1. Tarek Emam
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  2. S. I. Ali
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Correspondence to Tarek Emam.

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Emam, T., Ali, S.I. Norm–based approximation in E-[0,1] convex multi-objective programming. Calcolo 53, 723–735 (2016). https://doi.org/10.1007/s10092-015-0170-z

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  • DOI: https://doi.org/10.1007/s10092-015-0170-z

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