Smaller SDP for SOS decomposition
نویسندگان
چکیده
منابع مشابه
Block SOS Decomposition
Awidely usedmethod for determiningwhether amultivariate polynomial is a sum of squares of polynomials (SOS), called SOS decomposition, is to decide the feasibility of corresponding semi-definite programming (SDP) problem which can be efficiently solved in theory. In practice, although existing SDP solvers can work out some problems of big scale, the efficiency and reliability of such method dec...
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We investigate the relationships between various sum of squares (SOS) and semidefinite programming (SDP) relaxations for the sensor network localization problem. In particular, we show that Biswas and Ye’s SDP relaxation is equivalent to the degree one SOS relaxation of Kim et al. We also show that Nie’s sparse-SOS relaxation is stronger than the edge-based semidefinite programming (ESDP) relax...
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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 i...
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ژورنال
عنوان ژورنال: Journal of Global Optimization
سال: 2015
ISSN: 0925-5001,1573-2916
DOI: 10.1007/s10898-015-0300-9