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A regularized strong duality for nonsymmetric semidefinite least squares problem

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044, People’s Republic of China

    Yingnan Wang, Naihua Xiu & Ziyan Luo

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  1. Yingnan Wang
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  2. Naihua Xiu
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  3. Ziyan Luo
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Correspondence to Yingnan Wang.

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Wang, Y., Xiu, N. & Luo, Z. A regularized strong duality for nonsymmetric semidefinite least squares problem. Optim Lett 5, 665–682 (2011). https://doi.org/10.1007/s11590-010-0233-7

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  • DOI: https://doi.org/10.1007/s11590-010-0233-7

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