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论文类型：期刊论文
发表时间：2008-08-01
发表刊物：MATHEMATICAL PROGRAMMING
收录刊物：SCIE、EI、Scopus
卷号：114
期号：2
页面范围：349-391
ISSN号：0025-5610
关键字：nonlinear semidefinite programming; rate of convergence; the augmented Lagrangian method; variational analysis
摘要：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 (c) over bar > 0.