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

Xiangkai Sun (), Wen Tan () and Kok Lay Teo ()
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Xiangkai Sun: Chongqing Technology and Business University
Wen Tan: Chongqing Technology and Business University
Kok Lay Teo: Sunway University

Journal of Optimization Theory and Applications, 2023, vol. 197, issue 2, No 12, 737-764

Abstract: 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.

Keywords: SOS-convex polynomial optimization; Sum of squares conditions; Robust optimization; 90C22; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02184-6

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