Recovering optimal solutions via SOC-SDP relaxation of trust region subproblem with nonintersecting linear constraints
| Autor: | Shu-Cherng Fang, Jinyu Dai, Wenxun Xing |
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| Rok vydání: | 2019 |
| Předmět: |
Unit sphere
0209 industrial biotechnology Trust region 021103 operations research Control and Optimization Rank (linear algebra) Applied Mathematics Strategy and Management 0211 other engineering and technologies 02 engineering and technology Slater's condition Atomic and Molecular Physics and Optics Matrix decomposition Combinatorics Linear inequality 020901 industrial engineering & automation Relaxation (approximation) Business and International Management Electrical and Electronic Engineering Mathematics Complement (set theory) |
| Zdroj: | Journal of Industrial & Management Optimization. 15:1677-1699 |
| ISSN: | 1553-166X |
| DOI: | 10.3934/jimo.2018117 |
| Popis: | In this paper, we study an extended trust region subproblem (eTRS) in which the unit ball intersects with \begin{document}$m$\end{document} linear inequality constraints. In the literature, Burer et al. proved that an SOC-SDP relaxation (SOCSDPr) of eTRS is exact, under the condition that the nonredundant constraints do not intersect each other in the unit ball. Furthermore, Yuan et al. gave a necessary and sufficient condition for the corresponding SOCSDPr to be a tight relaxation when \begin{document}$m = 2$\end{document} . However, there lacks a recovering algorithm to generate an optimal solution of eTRS from an optimal solution \begin{document}$X^*$\end{document} of SOCSDPr when rank \begin{document}$(X^*)≥ 2$\end{document} and \begin{document}$m≥ 3$\end{document} . This paper provides such a recovering algorithm to complement those known works. |
| Databáze: | OpenAIRE |
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