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

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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.

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Authors and Affiliations

  1. Chongqing Key Laboratory of Social Economy and Applied Statistics, College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China

    Xiangkai Sun & Wen Tan

  2. School of Mathematical Sciences, Sunway University, 47500, Bandar Sunway, Selangor DarulEhsan, Malaysia

    Kok Lay Teo

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  1. Xiangkai Sun
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  2. Wen Tan
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Correspondence to Xiangkai Sun.

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Funding

This research was supported by the Natural Science Foundation of Chongqing (cstc2020jcyj-msxmX0016), the Science and Technology Research Program of Chongqing Municipal Education Commission (KJZDK202100803), the ARC Discovery Grant (DP190103361), the Education Committee Project Foundation of Chongqing for Bayu Young Scholar, and the Innovation Project of CTBU (yjscxx2022-112-71).

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Communicated by Alper Yildirim.

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Sun, X., Tan, W. & Teo, K.L. Characterizing a Class of Robust Vector Polynomial Optimization via Sum of Squares Conditions. J Optim Theory Appl 197, 737–764 (2023). https://doi.org/10.1007/s10957-023-02184-6

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