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

Author

Listed:
  • Liguo Jiao

    (Pusan National University)

  • Jae Hyoung Lee

    (Pukyong National University)

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.

Suggested Citation

  • Liguo Jiao & Jae Hyoung Lee, 2021. "Finding efficient solutions in robust multiple objective optimization with SOS-convex polynomial data," Annals of Operations Research, Springer, vol. 296(1), pages 803-820, January.
    • Handle: RePEc:spr:annopr:v:296:y:2021:i:1:d:10.1007_s10479-019-03216-z
    DOI: 10.1007/s10479-019-03216-z
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    References listed on IDEAS

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    1. Jae Hyoung Lee & Gue Myung Lee, 2018. "On optimality conditions and duality theorems for robust semi-infinite multiobjective optimization problems," Annals of Operations Research, Springer, vol. 269(1), pages 419-438, October.
    2. Erin K. Doolittle & Hervé L. M. Kerivin & Margaret M. Wiecek, 2018. "Robust multiobjective optimization with application to Internet routing," Annals of Operations Research, Springer, vol. 271(2), pages 487-525, December.
    3. Jae Hyoung Lee & Liguo Jiao, 2018. "Solving Fractional Multicriteria Optimization Problems with Sum of Squares Convex Polynomial Data," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 428-455, February.
    4. Jonas Ide & Anita Schöbel, 2016. "Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 235-271, January.
    5. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
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    Cited by:

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    2. Xiangkai Sun & Wen Tan & Kok Lay Teo, 2023. "Characterizing a Class of Robust Vector Polynomial Optimization via Sum of Squares Conditions," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 737-764, May.
    3. Zhe Hong & Kwan Deok Bae & Do Sang Kim, 2022. "Minimax programming as a tool for studying robust multi-objective optimization problems," Annals of Operations Research, Springer, vol. 319(2), pages 1589-1606, December.

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