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

Jae Hyoung Lee () and Liguo Jiao ()
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Jae Hyoung Lee: Pukyong National University
Liguo Jiao: Yanbian University

Journal of Optimization Theory and Applications, 2018, vol. 176, issue 2, No 9, 428-455

Abstract: 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.

Keywords: Fractional programming; Multicriteria optimization; Semidefinite programming; Sum of square convex polynomials; 90C32; 90C29; 65K05; 90C22 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10957-018-1222-8

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