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Characterizing a Class of Robust Vector Polynomial Optimization via Sum of Squares Conditions

Author

Listed:
  • Xiangkai Sun

    (Chongqing Technology and Business University)

  • Wen Tan

    (Chongqing Technology and Business University)

  • Kok Lay Teo

    (Sunway University)

Abstract

This paper deals with an SOS-convex (sum of squares convex) polynomial optimization problem with spectrahedral uncertain data in both the objective and constraints. By using a robust-type characteristic cone constraint qualification, we first obtain necessary and sufficient conditions for robust weakly efficient solutions of this uncertain SOS-convex polynomial optimization problem in terms of sum of squares conditions and linear matrix inequalities. Then, we propose a relaxation dual problem for this uncertain SOS-convex polynomial optimization problem and explore weak and strong duality properties between them. Moreover, we give a numerical example to show that the relaxation dual problem can be reformulated as a semidefinite linear programming problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:197:y:2023:i:2:d:10.1007_s10957-023-02184-6
    DOI: 10.1007/s10957-023-02184-6
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    References listed on IDEAS

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