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2008

The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming

8 years 5 months ago
The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming
We analyze the rate of local convergence of the augmented Lagrangian method for 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 certain 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 is proportional to 1/c, where c is the penalty parameter that exceeds a threshold c > 0. Key words: The augmented Lagrangian method, nonlinear semidefinite programming, rate of convergence, variational analysis.
Defeng Sun, Jie Sun, Liwei Zhang
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2008
Where MP
Authors Defeng Sun, Jie Sun, Liwei Zhang
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