Abstract
Semidefinite programming (SDP) is one of the most active areas in mathematical programming, due to varied applications and the availability of interior point algorithms. In this paper we propose a new pre-processing technique for SDP instances that exhibit algebraic symmetry. We present computational results to show that the solution times of certain SDP instances may be greatly reduced via the new approach.
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Acknowledgments
The authors are deeply indebted to Professor Masakazu Kojima for suggesting the outline of the proof of Theorem 4, and for making his Matlab implementation of Algorithm 4.1 in [21] available to them. The authors also thank an anonymous referee for pointing out erroneous numerical results in an earlier version of this paper.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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de Klerk, E., Dobre, C. & Ṗasechnik, D.V. Numerical block diagonalization of matrix *-algebras with application to semidefinite programming. Math. Program. 129, 91–111 (2011). https://doi.org/10.1007/s10107-011-0461-3
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DOI: https://doi.org/10.1007/s10107-011-0461-3