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December, 2019 Finding Efficient Solutions for Multicriteria Optimization Problems with SOS-convex Polynomials
Jae Hyoung Lee, Liguo Jiao
Taiwanese J. Math. 23(6): 1535-1550 (December, 2019). DOI: 10.11650/tjm/190101

Abstract

In this paper, we focus on the study of finding efficient solutions for a multicriteria optimization problem (MP), where both the objective and constraint functions are SOS-convex polynomials. By using the well-known $\epsilon$-constraint method (a scalarization technique), we substitute the problem (MP) to a class of scalar ones. Then, a zero duality gap result for each scalar problem, its sum of squares polynomial relaxation dual problem, the semidefinite representation of this dual problem, and the dual problem of the semidefinite programming problem, is established, under a suitable regularity condition. Moreover, we prove that an optimal solution of each scalar problem can be found by solving its associated semidefinite programming problem. As a consequence, we show that finding efficient solutions for the problem (MP) is tractable by employing the $\epsilon$-constraint method. A numerical example is also given to illustrate our results.

Citation

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Jae Hyoung Lee. Liguo Jiao. "Finding Efficient Solutions for Multicriteria Optimization Problems with SOS-convex Polynomials." Taiwanese J. Math. 23 (6) 1535 - 1550, December, 2019. https://doi.org/10.11650/tjm/190101

Information

Received: 1 April 2018; Revised: 29 November 2018; Accepted: 2 January 2019; Published: December, 2019
First available in Project Euclid: 8 January 2019

zbMATH: 07142985
MathSciNet: MR4033557
Digital Object Identifier: 10.11650/tjm/190101

Subjects:
Primary: 52A41 , 65K05 , 90C29

Keywords: $\epsilon$-constraint method , multicriteria optimization , semidefinite programming , SOS-convex polynomials

Rights: Copyright © 2019 The Mathematical Society of the Republic of China

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Vol.23 • No. 6 • December, 2019
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