On semidefinite programming relaxations for a class of robust SOS-convex polynomial optimization problems

Xiangkai Sun (), Jiayi Huang () and Kok Lay Teo ()
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Xiangkai Sun: Chongqing Technology and Business University
Jiayi Huang: Chongqing Technology and Business University
Kok Lay Teo: Sunway University

Journal of Global Optimization, 2024, vol. 88, issue 3, No 8, 755-776

Abstract: Abstract In this paper, we deal with a new class of SOS-convex (sum of squares convex) polynomial optimization problems with spectrahedral uncertainty data in both the objective and constraints. By using robust optimization and a weighted-sum scalarization methodology, we first present the relationship between robust solutions of this uncertain SOS-convex polynomial optimization problem and that of its corresponding scalar optimization problem. Then, by using a normal cone constraint qualification condition, we establish necessary and sufficient optimality conditions for robust weakly efficient solutions of this uncertain SOS-convex polynomial optimization problem based on scaled diagonally dominant sums of squares conditions and linear matrix inequalities. Moreover, we introduce a semidefinite programming relaxation problem of its weighted-sum scalar optimization problem, and show that robust weakly efficient solutions of the uncertain SOS-convex polynomial optimization problem can be found by solving the corresponding semidefinite programming relaxation problem.

Keywords: Convex polynomial optimization; Optimality conditions; Semidefinite programming relaxations; 90C25; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-023-01353-1

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