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An inexact spectral bundle method for convex quadratic semidefinite programming

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  • Huiling Lin

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Abstract

We present an inexact spectral bundle method for solving convex quadratic semidefinite optimization problems. This method is a first-order method, hence requires much less computational cost in each iteration than second-order approaches such as interior-point methods. In each iteration of our method, we solve an eigenvalue minimization problem inexactly, and solve a small convex quadratic semidefinite program as a subproblem. We give a proof of the global convergence of this method using techniques from the analysis of the standard bundle method, and provide a global error bound under a Slater type condition for the problem in question. Numerical experiments with matrices of order up to 3000 are performed, and the computational results establish the effectiveness of this method. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Huiling Lin, 2012. "An inexact spectral bundle method for convex quadratic semidefinite programming," Computational Optimization and Applications, Springer, vol. 53(1), pages 45-89, September.
  • Handle: RePEc:spr:coopap:v:53:y:2012:i:1:p:45-89
    DOI: 10.1007/s10589-011-9443-x
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    File URL: http://hdl.handle.net/10.1007/s10589-011-9443-x
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    References listed on IDEAS

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    1. Grégory Emiel & Claudia Sagastizábal, 2010. "Incremental-like bundle methods with application to energy planning," Computational Optimization and Applications, Springer, vol. 46(2), pages 305-332, June.
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    1. repec:eee:apmaco:v:265:y:2015:i:c:p:635-651 is not listed on IDEAS

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