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Exploiting Sparsity in SDP Relaxation of Polynomial Optimization Problems

In: Handbook on Semidefinite, Conic and Polynomial Optimization

Author

Listed:
  • Sunyoung Kim

    (Ewha W. University)

  • Masakazu Kojima

    (Tokyo Institute of Technology)

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.

Suggested Citation

  • Sunyoung Kim & Masakazu Kojima, 2012. "Exploiting Sparsity in SDP Relaxation of Polynomial Optimization Problems," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 499-531, Springer.
    • Handle: RePEc:spr:isochp:978-1-4614-0769-0_18
    DOI: 10.1007/978-1-4614-0769-0_18
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