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

Solving Fractional Multicriteria Optimization Problems with Sum of Squares Convex Polynomial Data 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Optimization Theory and Applications Springer Journals

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

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operations Research/Decision Theory
ISSN
0022-3239
eISSN
1573-2878
D.O.I.
10.1007/s10957-018-1222-8
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Optimization Theory and ApplicationsSpringer Journals

Published: Jan 23, 2018

References

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