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Properties of the Augmented Lagrangian in Nonlinear Semidefinite Optimization

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Abstract

We study the properties of the augmented Lagrangian function for nonlinear semidefinite programming. It is shown that, under a set of sufficient conditions, the augmented Lagrangian algorithm is locally convergent when the penalty parameter is larger than a certain threshold. An error estimate of the solution, depending on the penalty parameter, is also established.

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Authors and Affiliations

  1. Department of Decision Sciences and Singapore-MIT Alliance, National University of Singapore, Kent Ridge, Singapore

    J. Sun (Professor)

  2. Department of Applied Mathematics, Dalian University of Technology, Dalian, China

    L. W. Zhang (Professor)

  3. School of Management, University of Southampton, Highfield Southampton, United Kingdom

    Y. Wu (Lecturer)

Authors
  1. J. Sun
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  2. L. W. Zhang
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  3. Y. Wu
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Additional information

Communicated by P. Tseng

The first author was partially supported by Singapore-MIT Alliance and by the National University of Singapore under Grants RP314000-028/042/057-112. The second author was partially supported by the Funds of the Ministry of Education of China for PhD Units under Grant 20020141013 and the National Natural Science Foundation of China under Grant 10471015.

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Sun, J., Zhang, L.W. & Wu, Y. Properties of the Augmented Lagrangian in Nonlinear Semidefinite Optimization. J Optim Theory Appl 129, 437–456 (2006). https://doi.org/10.1007/s10957-006-9078-8

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  • DOI: https://doi.org/10.1007/s10957-006-9078-8

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