Conic Relaxations with Stable Exactness Conditions for Parametric Robust Convex Polynomial Problems

Thai Doan Chuong () and José Vicente-Pérez ()
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Thai Doan Chuong: Saigon University
José Vicente-Pérez: Universidad de Alicante

Journal of Optimization Theory and Applications, 2023, vol. 197, issue 2, No 1, 387-410

Abstract: Abstract In this paper, we examine stable exact relaxations for classes of parametric robust convex polynomial optimization problems under affinely parameterized data uncertainty in the constraints. We first show that a parametric robust convex polynomial problem with convex compact uncertainty sets enjoys stable exact conic relaxations under the validation of a characteristic cone constraint qualification. We then show that such stable exact conic relaxations become stable exact semidefinite programming relaxations for a parametric robust SOS-convex polynomial problem, where the uncertainty sets are assumed to be bounded spectrahedra. In addition, under the corresponding constraint qualification, we derive stable exact second-order cone programming relaxations for some classes of parametric robust convex quadratic programs under ellipsoidal uncertainty sets.

Keywords: Robust optimization; Convex polynomial; Stable exact relaxation; Spectrahedral uncertainty set; Conic relaxation; 49K99; 65K10; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02197-1

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