Lower Bounds on Matrix Factorization Ranks via Noncommutative Polynomial Optimization

Sander Gribling, David de Laat, Monique Laurent

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Abstract

We use techniques from (tracial noncommutative) polynomial optimization to formulate hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In particular, we consider the nonnegative rank, the positive semidefinite rank, and their symmetric analogues: the completely positive rank and the completely positive semidefinite rank. We study the convergence properties of our hierarchies, compare them extensively to known lower bounds, and provide some (numerical) examples.
Original languageEnglish
Place of PublicationIthaca
PublisherCornell University Library
Number of pages45
Publication statusPublished - 4 Aug 2017

Publication series

NamearXiv
Volume1708.01573

Keywords

  • optimization and control

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  • Research Output

    Lower bounds on matrix factorization ranks via noncommutative polynomial optimization

    Gribling, S., De Laat, D. & Laurent, M., Oct 2019, In : Foundations of Computational Mathematics. 19, 5, p. 1013-1070

    Research output: Contribution to journalArticleScientificpeer-review

    Open Access
  • Cite this

    Gribling, S., Laat, D. D., & Laurent, M. (2017). Lower Bounds on Matrix Factorization Ranks via Noncommutative Polynomial Optimization. (arXiv; Vol. 1708.01573). Cornell University Library.