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Solving Fractional Multicriteria Optimization Problems with Sum of Squares Convex Polynomial Data

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Abstract

This paper focuses on the study of finding efficient solutions in fractional multicriteria optimization problems with sum of squares convex polynomial data. We first relax the fractional multicriteria optimization problems to fractional scalar ones. Then, using the parametric approach, we transform the fractional scalar problems into non-fractional problems. Consequently, we prove that, under a suitable regularity condition, the optimal solution of each non-fractional scalar problem can be found by solving its associated single semidefinite programming problem. Finally, we show that finding efficient solutions in the fractional multicriteria optimization problems is tractable by employing the epsilon constraint method. In particular, if the denominators of each component of the objective functions are same, then we observe that efficient solutions in such a problem can be effectively found by using the hybrid method. Some numerical examples are given to illustrate our results.

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Acknowledgements

The authors would like to express their sincere thanks to the associate editor and anonymous referees for their valuable suggestions and constructive comments, which helped to improve the quality of the paper. Besides, the authors thank Professor Franco Giannessi for his very important comments.

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Authors and Affiliations

  1. Department of Applied Mathematics, Pukyong National University, Busan, 48513, Republic of Korea

    Jae Hyoung Lee

  2. Department of Mathematics, College of Science, Yanbian University, Yanji City, 133002, Jilin Province, China

    Liguo Jiao

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  1. Jae Hyoung Lee
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  2. Liguo Jiao
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Correspondence to Liguo Jiao.

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Lee, J.H., Jiao, L. Solving Fractional Multicriteria Optimization Problems with Sum of Squares Convex Polynomial Data. J Optim Theory Appl 176, 428–455 (2018). https://doi.org/10.1007/s10957-018-1222-8

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  • DOI: https://doi.org/10.1007/s10957-018-1222-8

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