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

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 betwe...

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Veröffentlicht in:Journal of global optimization Jg. 88; H. 3; S. 755 - 776
Hauptverfasser: Sun, Xiangkai, Huang, Jiayi, Teo, Kok Lay
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.03.2024
Springer
Springer Nature B.V
Schlagworte:
Computer Science
Convex analysis
Linear matrix inequalities
Mathematical analysis
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Polynomials
Programming
Real Functions
Robustness
Semidefinite programming
Convex polynomial optimization
Optimality conditions
90C29
Semidefinite programming relaxations
90C46
90C25
ISSN:0925-5001, 1573-2916
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-023-01353-1