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Minimax Theory and its Applications 04 (2019), No. 2, 329--339
Copyright Heldermann Verlag 2019

An Elementary Proof for the Exact Relaxation for Rank One Moment Matrices in Multi-Polynomial SOS Relaxation

Shenglong Hu
Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou 310018, China

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.

Keywords: Multi-polynomial, multi-form, SOS, exact relaxation.

MSC: 15A18, 15A42, 15A69

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