Conic Relaxations with Stable Exactness Conditions for Parametric Robust Convex Polynomial Problems
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Title: | Conic Relaxations with Stable Exactness Conditions for Parametric Robust Convex Polynomial Problems |
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Authors: | Chuong, Thai Doan | Vicente-Pérez, José |
Research Group/s: | Laboratorio de Optimización (LOPT) |
Center, Department or Service: | Universidad de Alicante. Departamento de Matemáticas |
Keywords: | Robust optimization | Convex polynomial | Stable exact relaxation | Spectrahedral uncertainty set | Conic relaxation |
Issue Date: | 24-Mar-2023 |
Publisher: | Springer Nature |
Citation: | Journal of Optimization Theory and Applications. 2023, 197: 387-410. https://doi.org/10.1007/s10957-023-02197-1 |
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. |
Sponsor: | Chuong was supported by the National Foundation for Science and Technology Development of Vietnam (NAFOSTED) under grant number 101.01−2020.09. Research of J. Vicente-Pérez was partially supported by the Ministry of Science, Innovation and Universities of Spain and the European Regional Development Fund (ERDF) of the European Commission, Grant PGC2018-097960-B-C22, and by the Generalitat Valenciana, Grant AICO/2021/165. |
URI: | http://hdl.handle.net/10045/133861 |
ISSN: | 0022-3239 (Print) | 1573-2878 (Online) |
DOI: | 10.1007/s10957-023-02197-1 |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023 |
Peer Review: | si |
Publisher version: | https://doi.org/10.1007/s10957-023-02197-1 |
Appears in Collections: | INV - LOPT - Artículos de Revistas |
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Chuong_Vicente-Perez_2023_JOptimTheoryAppl_final.pdf | Versión final (acceso restringido) | 422,03 kB | Adobe PDF | Open Request a copy |
Chuong_Vicente-Perez_2023_JOptimTheoryAppl_preprint.pdf | Preprint (acceso abierto) | 402,99 kB | Adobe PDF | Open Preview |
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