- The Rate of Convergence of the Augmented Lagrangian Method for Nonlinear Semidefinite Programming Defeng Sun (matsundfnus.edu.sg) Jie Sun (jsunnus.edu.sg) Liwei Zhang (lwzhangdlut.edu.cn) Abstract: 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 $\overline{c}>0$. Keywords: The augmented Lagrangian method, nonlinear semidefinite programming, rate of convergence, variational analysis Category 1: Linear, Cone and Semidefinite Programming Category 2: Nonlinear Optimization Citation: Technical Report, Department of Mathematics, National University of Singapore, January 2006. Download: [PDF]Entry Submitted: 01/25/2006Entry Accepted: 01/25/2006Entry Last Modified: 01/25/2006Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.