Rank-one matrix completion is solved by the sum-of-squares relaxation of order two
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...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Institute of Electrical and Electronics Engineers (IEEE)
2017
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| Online Access: | http://hdl.handle.net/1721.1/110289 https://orcid.org/0000-0001-7052-5097 |
| Summary: | 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. |
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