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Exploiting Sparsity in SDP Relaxation of Polynomial Optimization Problems

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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 survey on the sparse SDP relaxation proposed as a sparse variant of Lasserre’s SDP relaxation of polynomial optimization problems. We discuss the primal approach to derive the sparse SDP relaxation by exploiting the structured sparsity. In addition, numerical techniques used in the Matlab package SparsePOP for solving POPs are presented. We report numerical results on SparsePOP and the application of the sparse SDP relaxation to sensor network localization problems.

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Acknowledgements

S. Kim’s research was supported by NRF 2009-007-1314 and NRF 2010-000-8784.  M. Kojima’s research was supported by Grant-in-Aid for Scientific Research (B) 22310089.

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Authors and Affiliations

  1. Department of Mathematics, Ewha W. University, 11-1 DaHyun-Dong, SuhDaeMoon-Gu, Seoul, Korea, 120-750

    Sunyoung Kim

  2. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1-W8-29, Oh-Okayama, Meguro, Tokyo, 152-8552, Japan

    Masakazu Kojima

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  1. Sunyoung Kim
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Correspondence to Sunyoung Kim .

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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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Kim, S., Kojima, M. (2012). Exploiting Sparsity in SDP Relaxation of Polynomial Optimization Problems. 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_18

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