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August, 2020 Multi-objective Optimization Problems with SOS-convex Polynomials over an LMI Constraint
Liguo Jiao, Jae Hyoung Lee, Yuto Ogata, Tamaki Tanaka
Taiwanese J. Math. 24(4): 1021-1043 (August, 2020). DOI: 10.11650/tjm/191002

Abstract

In this paper, we aim to find efficient solutions of a multi-objective optimization problem over a linear matrix inequality (LMI in short), in which the objective functions are SOS-convex polynomials. We do this by using two scalarization approaches, that is, the $\epsilon$-constraint method and the hybrid method. More precisely, we first transform the considered multi-objective optimization problem into their scalar forms by the $\epsilon$-constraint method and the hybrid method, respectively. Then, strong duality results, between each formulated scalar problem and its associated semidefinite programming dual problem, are given, respectively. Moreover, for each proposed scalar problem, we show that its optimal solution can be found by solving an associated single semidefinite programming problem, under a suitable regularity condition. As a consequence, we prove that finding efficient solutions to the considered problem can be done by employing any of the two scalarization approaches. Besides, we illustrate our methods through some nontrivial numerical examples.

Citation

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Liguo Jiao. Jae Hyoung Lee. Yuto Ogata. Tamaki Tanaka. "Multi-objective Optimization Problems with SOS-convex Polynomials over an LMI Constraint." Taiwanese J. Math. 24 (4) 1021 - 1043, August, 2020. https://doi.org/10.11650/tjm/191002

Information

Received: 7 April 2019; Revised: 18 August 2019; Accepted: 20 October 2019; Published: August, 2020
First available in Project Euclid: 30 October 2019

MathSciNet: MR4124556
Digital Object Identifier: 10.11650/tjm/191002

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

Rights: Copyright © 2020 The Mathematical Society of the Republic of China

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Vol.24 • No. 4 • August, 2020
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