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Global convergence of modified augmented Lagrangian methods for nonlinear semidefinite programming |
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| Authors: | Huixian Wu Hezhi Luo Xiaodong Ding Guanting Chen |
| Institution: | 1. Department of Mathematics, College of Science, Hangzhou Dianzi University, Hangzhou, 310018, Zhejiang, People’s Republic of China 2. Department of Applied Mathematics, College of Science, Zhejiang University of Technology, Hangzhou, 310032, Zhejiang, People’s Republic of China |
| Abstract: | We investigate in this paper global convergence properties of the augmented Lagrangian method for nonlinear semidefinite programming (NLSDP). Four modified augmented Lagrangian methods for solving NLSDP based on different algorithmic strategies are proposed. Possibly infeasible limit points of the proposed methods are characterized. It is proved that feasible limit points that satisfy the Mangasarian-Fromovitz constraint qualification are KKT points of NLSDP without requiring the boundedness condition of the multipliers. Preliminary numerical results are reported to compare the performance of the modified augmented Lagrangian methods. |
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