Taiwanese Journal of Mathematics

Finding Efficient Solutions for Multicriteria Optimization Problems with SOS-convex Polynomials

Jae Hyoung Lee and Liguo Jiao

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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.

Article information

Source
Taiwanese J. Math., Advance publication (2019), 16 pages.

Dates
First available in Project Euclid: 8 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1546938169

Digital Object Identifier
doi:10.11650/tjm/190101

Subjects
Primary: 90C29: Multi-objective and goal programming 65K05: Mathematical programming methods [See also 90Cxx] 52A41: Convex functions and convex programs [See also 26B25, 90C25]

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

Citation

Lee, Jae Hyoung; Jiao, Liguo. Finding Efficient Solutions for Multicriteria Optimization Problems with SOS-convex Polynomials. Taiwanese J. Math., advance publication, 8 January 2019. doi:10.11650/tjm/190101. https://projecteuclid.org/euclid.twjm/1546938169


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