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A utopia point method-based robust vector polynomial optimization scheme

Author

Listed:
  • Tianyi Han

    (Shanghai Jiao Tong University)

  • Liguo Jiao

    (Northeast Normal University
    Institute of Applied Physics and Computational Mathematics)

  • Jae Hyoung Lee

    (Pukyong National University)

  • Junping Yin

    (Institute of Applied Physics and Computational Mathematics
    Shanghai Zhangjiang Institute of Mathematics)

Abstract

In this paper, we focus on a class of robust vector polynomial optimization problems (RVPOP in short) without any convex assumptions. By combining/improving the utopia point method (a nonlinear scalarization) for vector optimization and “joint+marginal" relaxation method for polynomial optimization, we solve the RVPOP successfully. Both theoratical and computational aspects are considered.

Suggested Citation

  • Tianyi Han & Liguo Jiao & Jae Hyoung Lee & Junping Yin, 2024. "A utopia point method-based robust vector polynomial optimization scheme," Journal of Global Optimization, Springer, vol. 88(2), pages 461-483, February.
    • Handle: RePEc:spr:jglopt:v:88:y:2024:i:2:d:10.1007_s10898-023-01321-9
    DOI: 10.1007/s10898-023-01321-9
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    References listed on IDEAS

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    1. Gabriel R. Bitran, 1980. "Linear Multiple Objective Problems with Interval Coefficients," Management Science, INFORMS, vol. 26(7), pages 694-706, July.
    2. J. Lasserre, 2011. "Min-max and robust polynomial optimization," Journal of Global Optimization, Springer, vol. 51(1), pages 1-10, September.
    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. Feng Guo & Liguo Jiao, 2023. "A new scheme for approximating the weakly efficient solution set of vector rational optimization problems," Journal of Global Optimization, Springer, vol. 86(4), pages 905-930, August.
    5. J. Lasserre, 2012. "An algorithm for semi-infinite polynomial optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 119-129, April.
    6. Thai Doan Chuong, 2022. "Second-order cone programming relaxations for a class of multiobjective convex polynomial problems," Annals of Operations Research, Springer, vol. 311(2), pages 1017-1033, April.
    7. 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.
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