A Note on Sparse SOS and SDP Relaxations for Polynomial Optimization Problems over Symmetric Cones

Masakazu Koima (kojimais.titech.ac.jp)
Masakazu Muramatsu (muramatucs.uec.ac.jp)

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.

Keywords: Polynomial Optimization Problem, Conic Program, Symmetric Cone, Euclidean Jordan Algebra, Sum of Squares, Global Optimization, Semidefinite Program

Category 1: Global Optimization

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Research Report B-421, Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Meguro, Tokyo 152-8552, Japan, January 2006.

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Entry Submitted: 01/22/2006
Entry Accepted: 01/23/2006
Entry Last Modified: 01/24/2006

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