A regularized strong duality for nonsymmetric semidefinite least squares problem

作者：Wang Yingnan^*; Xiu Naihua; Luo Ziyan

来源：Optimization Letters, 2011, 5(4): 665-682.

DOI：10.1007/s11590-010-0233-7

• Nonsymmetric semidefinite least squares
• Strong duality
• Facial reduction algorithm
• Nonsingularity
• Constraint nondegeneracy

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.

• 出版日期2011-11
• 单位北京交通大学