Robust SOS-convex polynomial optimization problems: exact SDP relaxations
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Title: | Robust SOS-convex polynomial optimization problems: exact SDP relaxations |
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Authors: | Jeyakumar, Vaithilingam | Li, Guoyin | Vicente-Pérez, José |
Research Group/s: | Laboratorio de Optimización (LOPT) |
Center, Department or Service: | Universidad de Alicante. Departamento de Métodos Cuantitativos y Teoría Económica |
Keywords: | Robust optimization | SOS-convex polynomials | Semidefinite programming relaxations | Sums of squares polynomials |
Knowledge Area: | Fundamentos del Análisis Económico |
Issue Date: | Jan-2015 |
Publisher: | Springer Berlin Heidelberg |
Citation: | Optimization Letters. 2015, 9(1): 1-18. doi:10.1007/s11590-014-0732-z |
Abstract: | This paper studies robust solutions and semidefinite linear programming (SDP) relaxations of a class of convex polynomial optimization problems in the face of data uncertainty. The class of convex optimization problems, called robust SOS-convex polynomial optimization problems, includes robust quadratically constrained convex optimization problems and robust separable convex polynomial optimization problems. It establishes sums-of-squares polynomial representations characterizing robust solutions and exact SDP-relaxations of robust SOS-convex polynomial optimization problems under various commonly used uncertainty sets. In particular, the results show that the polytopic and ellipsoidal uncertainty sets, that allow second-order cone re-formulations of robust quadratically constrained optimization problems, continue to permit exact SDP-relaxations for a broad class of robust SOS-convex polynomial optimization problems. |
Sponsor: | Research was partially supported by a grant from the Australian Research Council. J. Vicente-Pérez has been partially supported by the MICINN of Spain, Grant MTM2011-29064-C03-02. |
URI: | http://hdl.handle.net/10045/51992 |
ISSN: | 1862-4472 (Print) | 1862-4480 (Online) |
DOI: | 10.1007/s11590-014-0732-z |
Language: | eng |
Type: | info:eu-repo/semantics/article |
Rights: | © Springer-Verlag Berlin Heidelberg 2014. The final publication is available at Springer via http://dx.doi.org/10.1007/s11590-014-0732-z |
Peer Review: | si |
Publisher version: | http://dx.doi.org/10.1007/s11590-014-0732-z |
Appears in Collections: | INV - LOPT - Artículos de Revistas INV - DMCTE - Artículos de Revistas |
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2015_Jeyakumar_etal_OptimLett_final.pdf | Versión final (acceso restringido) | 232,07 kB | Adobe PDF | Open Request a copy |
2015_Jeyakumar_etal_OptimLett_preprint.pdf | Preprint (acceso abierto) | 186,92 kB | Adobe PDF | Open Preview |
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