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

Authors:
Masakazu Kojima;Masakazu Muramatsu
Affiliations:
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan 152-8552;Department of Computer Science, The University of Electro-Communications, Tokyo, Japan 182-8585
Venue:
Computational Optimization and Applications
Year:
2009

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Abstract

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.