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Successive Linearization Methods for Nonlinear Semidefinite Programs

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Abstract

We present a successive linearization method with a trust region-type globalization for the solution of nonlinear semidefinite programs. At each iteration, the method solves a quadratic semidefinite program, which can be converted to a linear semidefinite program with a second order cone constraint. A subproblem of this kind can be solved quite efficiently by using some recent software for semidefinite and second-order cone programs. The method is shown to be globally convergent under certain assumptions. Numerical results on some nonlinear semidefinite programs including optimization problems with bilinear matrix inequalities are reported to illustrate the behaviour of the proposed method.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Statistics, University of Würzburg, Am Hubland, 97074, Würzburg, Germany

    Christian Kanzow & Christian Nagel

  2. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Hirokazu Kato & Masao Fukushima

Authors
  1. Christian Kanzow
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  2. Christian Nagel
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  3. Hirokazu Kato
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  4. Masao Fukushima
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Corresponding author

Correspondence to Christian Kanzow.

Additional information

The research of the fourth author was supported in part by a Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science. The research of the second author was supported by the DFG (Deutsche Forschungsgemeinschaft).

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Kanzow, C., Nagel, C., Kato, H. et al. Successive Linearization Methods for Nonlinear Semidefinite Programs. Comput Optim Applic 31, 251–273 (2005). https://doi.org/10.1007/s10589-005-3231-4

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  • DOI: https://doi.org/10.1007/s10589-005-3231-4

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