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Global convergence of modified augmented Lagrangian methods for nonlinear semidefinite programming

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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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Acknowledgements

The authors would like to thank the two anonymous referees for the detailed comments and valuable suggestions which have improved the final presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Hangzhou Dianzi University, Hangzhou, 310018, Zhejiang, People’s Republic of China

    Huixian Wu & Guanting Chen

  2. Department of Applied Mathematics, College of Science, Zhejiang University of Technology, Hangzhou, 310032, Zhejiang, People’s Republic of China

    Hezhi Luo & Xiaodong Ding

Authors
  1. Huixian Wu
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  2. Hezhi Luo
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  3. Xiaodong Ding
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  4. Guanting Chen
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Correspondence to Hezhi Luo.

Additional information

This work was jointly supported by the National Natural Science Foundation of China under grant 11071219, the Postdoctoral Key Research Foundation of China under grant 201003242, and the Zhejiang Provincial Natural Science Foundation of China under grants Y13A010077 and Y13A010050.

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Wu, H., Luo, H., Ding, X. et al. Global convergence of modified augmented Lagrangian methods for nonlinear semidefinite programming. Comput Optim Appl 56, 531–558 (2013). https://doi.org/10.1007/s10589-013-9568-1

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