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Title: The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming
Authors: Sun, D. 
Sun, J. 
Zhang, L.
Keywords: Nonlinear semidefinite programming
Rate of convergence
The augmented Lagrangian method
Variational analysis
Issue Date: 2008
Citation: Sun, D., Sun, J., Zhang, L. (2008). The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming. Mathematical Programming 114 (2) : 349-391. ScholarBank@NUS Repository.
Abstract: We analyze the rate of local convergence of the augmented Lagrangian method in nonlinear semidefinite optimization. The presence of the positive semidefinite cone constraint requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and variational analysis on the projection operator in the symmetric matrix space. Without requiring strict complementarity, we prove that, under the constraint nondegeneracy condition and the strong second order sufficient condition, the rate of convergence is linear and the ratio constant is proportional to 1/c, where c is the penalty parameter that exceeds a threshold c̄ > 0 . © 2007 Springer-Verlag.
Source Title: Mathematical Programming
ISSN: 00255610
DOI: 10.1007/s10107-007-0105-9
Appears in Collections:Staff Publications

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