Abstract
When using interior point methods for solving semidefinite programs (SDP), one needs to solve a system of linear equations at each iteration. For problems of large size, solving the system of linear equations can be very expensive. In this paper, we propose a trust region algorithm for solving SDP problems. At each iteration we perform a number of conjugate gradient iterations, but do not need to solve a system of linear equations. Under mild assumptions, the convergence of this algorithm is established. Numerical examples are given to illustrate the convergence results obtained.
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Acknowledgements
The authors would like to thank Professor Florian Jarre for his advice and guidance, and also the editor and three referees for their helpful comments.
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This work is supported by National Natural Science Foundation of China 10971162.
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Huang, A., Xu, C. A trust region method for solving semidefinite programs. Comput Optim Appl 55, 49–71 (2013). https://doi.org/10.1007/s10589-012-9514-7
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DOI: https://doi.org/10.1007/s10589-012-9514-7