On the convergence of augmented Lagrangian methods for nonlinear semidefinite programming

Authors:
H. Z. Luo;H. X. Wu;G. T. Chen
Affiliations:
Department of Applied Mathematics, College of Science, Zhejiang University of Technology, Hangzhou, People's Republic of China 310032;Department of Mathematics, College of Science, Hangzhou Dianzi University, Hangzhou, People's Republic of China 310018;Department of Mathematics, College of Science, Hangzhou Dianzi University, Hangzhou, People's Republic of China 310018
Venue:
Journal of Global Optimization
Year:
2012

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Abstract

In this paper, we present new convergence properties of the augmented Lagrangian method for nonlinear semidefinite programs (NSDP). Convergence to the approximately global solutions and optimal values of NSDP is first established for a basic augmented Lagrangian scheme under mild conditions, without requiring the boundedness condition of the multipliers. We then propose four modified augmented Lagrangian methods for NSDP based on different algorithmic strategies. We show that the same convergence of the proposed methods can be ensured under weaker conditions.