A regularized strong duality for nonsymmetric semidefinite least squares problem
A regularized strong duality for nonsymmetric semidefinite least squares problem
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DOI：
10.1007/s11590-010-0233-7
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发表时间：
2011-11
影响因子：
1.6
通讯作者：
Yingnan Wang;N. Xiu;Ziyan Luo
中科院分区：
文献类型：
--
作者：
Yingnan Wang;N. Xiu;Ziyan Luo
非对称半定最小二乘问题（NSDLS）是寻找一个在Frobenius范数下最接近给定矩阵的非对称半定矩阵。它是半定最小二乘问题（SDLS）的推广，在机器人和自动化领域有重要的应用。本文通过建立带线性约束的锥的极小表示，得到了NSDLS的一个正则化的强对偶的低维投影。进一步，我们研究了对偶问题的一阶最优性系统的广义微分性质和非奇异性。这些理论结果表明，我们可以很好地解决NSDLS目前的拉格朗日对偶方法SDLS。
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.