Geodesic
An elementary proof for the exact relaxation for rank one moment matrices in multi-polynomial SOS relaxation
Minimax theory and its applications, Tome 4 (2019) no. 2
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We present an elementary proof for the fact that an optimal rank one moment matrix in the multi-polynomial SOS relaxation gives an exact relaxation. This fact is a fundamental result in multi-polynomial SOS relaxation method for the class of multi-polynomial optimization problems. The multi-polynomial SOS relaxation method is designed by exploring the special structures of the class of multi-polynomial optimization problems, which has the advantage for giving an SDP with size about half of that for the classical SOS relaxation in the general formulation.
Mots-clés : Multi-polynomial, multi-form, SOS, exact relaxation 
@article{MTA_2019_4_2_a5,
     author = {Shenglong Hu},
     title = {An elementary proof for the exact relaxation for rank one moment matrices in multi-polynomial {SOS} relaxation},
     journal = {Minimax theory and its applications},
     year = {2019},
     volume = {4},
     number = {2},
     zbl = {1450.49004},
     url = {http://geodesic.mathdoc.fr/item/MTA_2019_4_2_a5/}
}
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Shenglong Hu. An elementary proof for the exact relaxation for rank one moment matrices in multi-polynomial SOS relaxation. Minimax theory and its applications, Tome 4 (2019) no. 2. http://geodesic.mathdoc.fr/item/MTA_2019_4_2_a5/