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

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

Annals of Operations Research, 2021, vol. 296, issue 1, No 31, 803-820

Abstract: Abstract 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 $$\epsilon $$ 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.

Keywords: Multiobjective optimization; Robust optimization; Semidefinite programming relaxations; SOS-convex polynomials; 90C29; 90C22; 52A41 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10479-019-03216-z

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