Finding efficient solutions in robust multiple objective optimization with SOS-convex polynomial data

In this article, a mathematical programming problem under affinely parameterized uncertain data with multiple objective functions given by SOS-convex polynomials, denoting by (UMP), is considered; moreover, its robust counterpart, denoting by (RMP), is proposed by following the robust optimization a...

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Vydané v:Annals of operations research Ročník 296; číslo 1-2; s. 803 - 820
Hlavní autori: Jiao, Liguo, Lee, Jae Hyoung
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.01.2021
Springer
Springer Nature B.V
Predmet:
Business and Management
Combinatorics
Functions (mathematics)
Mathematical optimization
Mathematical programming
Methods
Multiple criteria decision making
Multiple objective analysis
Nonlinear programming
Operations research
Operations Research/Decision Theory
Optimization
Polynomials
Robustness (mathematics)
S.i.: Mopgp 2017
Theory of Computation
South Korea
Robust optimization
Semidefinite programming relaxations
52A41
SOS-convex polynomials
Multiobjective optimization
90C22
90C29
ISSN:0254-5330, 1572-9338
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Popis
Shrnutí:In this article, a mathematical programming problem under affinely parameterized uncertain data with multiple objective functions given by SOS-convex polynomials, denoting by (UMP), is considered; moreover, its robust counterpart, denoting by (RMP), is proposed by following the robust optimization approach (worst-case approach). Then, by employing the well-known ϵ -constraint method (a scalarization technique), we substitute (RMP) by a class of scalar problems. Under some suitable conditions, a zero duality gap result, between each scalar problem and its relaxation problems, is established; moreover, the relationship of their solutions is also discussed. As a consequence, we observe that finding robust efficient solutions to (UMP) is tractable by such a scalarization method. Finally, a nontrivial numerical example is designed to show how to find robust efficient solutions to (UMP) by applying our results.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-019-03216-z