An Elementary Proof for the Exact Relaxation for Rank One Moment Matrices in Multi-Polynomial SOS Relaxation
Keywords:
Multi-polynomial, multi-form, SOS, exact relaxation.Abstract
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.
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