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PENNON: Software for Linear and Nonlinear Matrix Inequalities

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Handbook on Semidefinite, Conic and Polynomial Optimization

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 166))

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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.

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Notes

  1. 1.

    plato.la.asu.edu/bench.html.

  2. 2.

    plato.asu.edu/ftp/sparse_sdp.html.

  3. 3.

    plato.asu.edu/ftp/sparse_sdp.html.

  4. 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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Authors and Affiliations

  1. School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK

    Michal Kocvara

  2. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodárenskou veží 4, 18208, Praha 8, Czech Republic

    Michal Kocvara

  3. Institute of Applied Mathematics, University of Erlangen-Nuremberg, Martensstrasse 3, 91058, Erlangen, Germany

    Michael Stingl

Authors
  1. Michal Kocvara
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  2. Michael Stingl
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Correspondence to Michal Kocvara .

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Editors and Affiliations

  1. Department of Mathematics and Industrial, Ecole Polytechnique Montreal, Édouard-Montpetit Boulevard 2350, Montreal, QC, Canada, H3C 3A7

    Miguel F. Anjos

  2. LAAS-CNRS, Avenue du Colonel Roche 7, 31077, Toulouse Cedex 4, France

    Jean B. Lasserre

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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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