Abstract
We present a collection of computer programs for the solution of linear and nonlinear semidefinite optimization problems. After briefly discussing the underlying algorithm, the generalized augmented Lagrangian method, we describe details of the specific programs for linear, bilinear and general nonlinear semidefinite optimization problems. For each of the programs we present typical application areas and examples.
Keywords
- Pennon
- Augmented Lagrangian
- Cholesky Method
- Hessian-vector Products
- Linear Semidefinite Programming Problem (LSDP)
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes
- 1.
plato.la.asu.edu/bench.html.
- 2.
plato.asu.edu/ftp/sparse_sdp.html.
- 3.
plato.asu.edu/ftp/sparse_sdp.html.
- 4.
See http://www.mathematik.uni-trier.de/ ∼ leibfritz/Proj_TestSet/NSDPTestSet.htm.
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Acknowledgements
The authors would like to thank Didier Henrion and Johan Löfbeg for their constant help during the code development. The work has been partly supported by grant A100750802 of the Czech Academy of Sciences (MK) and by DFG cluster of excellence 315 (MS). The manuscript was finished while the first author was visiting the Institute for Pure and Applied Mathematics, UCLA. The support and friendly atmosphere of the Institute are acknowledged with gratitude.
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Kocvara, M., Stingl, M. (2012). PENNON: Software for Linear and Nonlinear Matrix Inequalities. In: Anjos, M.F., Lasserre, J.B. (eds) Handbook on Semidefinite, Conic and Polynomial Optimization. International Series in Operations Research & Management Science, vol 166. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0769-0_26
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