Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization

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2013
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Theobald, Thorsten
Jansson Andrén, Lina
Lasserre, Jean B.
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Mathematics of Operations Research. 2013, 38(1), pp. 122-141. ISSN 0364-765X. eISSN 1526-5471. Available under: doi: 10.1287/moor.1120.0558
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In this paper we study various approaches for exploiting symmetries in polynomial optimization problems within the framework of semidefinite programming relaxations. Our special focus is on constrained problems especially when the symmetric group is acting on the variables. In particular, we investigate the concept of block decomposition within the framework of constrained polynomial optimization problems, show how the degree principle for the symmetric group can be computationally exploited, and also propose some methods to efficiently compute the geometric quotient.

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ISO 690RIENER, Cordian, Thorsten THEOBALD, Lina JANSSON ANDRÉN, Jean B. LASSERRE, 2013. Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization. In: Mathematics of Operations Research. 2013, 38(1), pp. 122-141. ISSN 0364-765X. eISSN 1526-5471. Available under: doi: 10.1287/moor.1120.0558
BibTex
@article{Riener2013Explo-23503,
  year={2013},
  doi={10.1287/moor.1120.0558},
  title={Exploiting Symmetries in SDP-Relaxations for Polynomial Optimization},
  number={1},
  volume={38},
  issn={0364-765X},
  journal={Mathematics of Operations Research},
  pages={122--141},
  author={Riener, Cordian and Theobald, Thorsten and Jansson Andrén, Lina and Lasserre, Jean B.}
}
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