A regularized strong duality for nonsymmetric semidefinite least squares problem

The nonsymmetric semidefinite least squares problem (NSDLS) is to find a nonsymmetric semidefinite matrix which is closest to a given matrix in Frobenius norm. It is an extension of the semidefinite least squares problem (SDLS) and has important application in the area of robotics and automation. In...

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Bibliographic Details
Published in:Optimization letters 2011-11, Vol.5 (4), p.665-682
Main Authors: Wang, Yingnan, Xiu, Naihua, Luo, Ziyan
Format: Article
Language:English
Subjects:
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
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Summary:The nonsymmetric semidefinite least squares problem (NSDLS) is to find a nonsymmetric semidefinite matrix which is closest to a given matrix in Frobenius norm. It is an extension of the semidefinite least squares problem (SDLS) and has important application in the area of robotics and automation. In this note, by developing the minimal representation of the underlying cone with the linear constraints, we obtain a regularized strong duality with low-dimensional projection for NSDLS. Further, we study the generalized differential properties and nonsingularity of the first order optimality system about the dual problem. These theoretical results demonstrate that we can solve NSDLS as good as the current Lagrangian dual approaches to SDLS.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-010-0233-7