Computational Optimization and Applications

, Volume 42, Issue 1, pp 31–41 | Cite as

A note on sparse SOS and SDP relaxations for polynomial optimization problems over symmetric cones

  • Masakazu Kojima
  • Masakazu Muramatsu


This short note extends the sparse SOS (sum of squares) and SDP (semidefinite programming) relaxation proposed by Waki, Kim, Kojima and Muramatsu for normal POPs (polynomial optimization problems) to POPs over symmetric cones, and establishes its theoretical convergence based on the recent convergence result by Lasserre on the sparse SOS and SDP relaxation for normal POPs. A numerical example is also given to exhibit its high potential.


Polynomial optimization problem Conic program Symmetric cone Euclidean Jordan algebra Sum of squares Global optimization Semidefinite program 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Mathematical and Computing SciencesTokyo Institute of TechnologyTokyoJapan
  2. 2.Department of Computer ScienceThe University of Electro-CommunicationsTokyoJapan

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