Rank-one matrix completion is solved by the sum-of-squares relaxation of order two
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Demanet_Rank-one matrix.pdf
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305.57 KB
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Author(s)
Cosse, Augustin
Demanet, Laurent
Date Issued
January 2016
Journal
2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Cosse, Augustin, and Laurent Demanet. “Rank-One Matrix Completion Is Solved by the Sum-of-Squares Relaxation of Order Two.” 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) (December 2015). ©2015 IEEE
Version
Author's final manuscript
Abstract
This note studies the problem of nonsymmetric rank-one matrix completion. We show that in every instance where the problem has a unique solution, one can recover the original matrix through the second round of the sum-of-squares/Lasserre hierarchy with minimization of the trace of the moments matrix. Our proof system is based on iteratively building a sum of N - 1 linearly independent squares, where N is the number of monomials of degree at most two, corresponding to the canonical basis (z[superscript α] - z[subscript 0][superscript α])[superscript 2]. Those squares are constructed from the ideal I generated by the constraints and the monomials provided by the minimization of the trace.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1109/CAMSAP.2015.7383723
