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

  • Liguo Jiao
  • Jae Hyoung LeeEmail author
S.I.: MOPGP 2017


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 \(\epsilon \)-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.


Multiobjective optimization Robust optimization Semidefinite programming relaxations SOS-convex polynomials 

Mathematics Subject Classification

90C29 90C22 52A41 



The authors would like to express their sincere thanks to anonymous referees for their very helpful and valuable suggestions and comments for the paper.


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Authors and Affiliations

  1. 1.Finance Fishery Manufacture Industrial Mathematics Center on Big DataPusan National UniversityBusanRepublic of Korea
  2. 2.Department of Applied MathematicsPukyong National UniversityBusanRepublic of Korea

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