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Other research product . Other ORP type . 2017

Lower bounds on matrix factorization ranks via noncommutative polynomial optimization

Gribling, Sander; Laat, David; Laurent, Monique;
Open Access
English
Published: 04 Aug 2017
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 completely positive rank, and their symmetric analogues: the positive semidefinite 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.
Funded by
NWO| Approximation Algorithms, Quantum Information and Semidefinite Optimization
Project
  • Funder: Netherlands Organisation for Scientific Research (NWO) (NWO)
  • Project Code: 2300181725
,
EC| QPROGRESS
Project
QPROGRESS
Progress in quantum computing: Algorithms, communication, and applications
  • Funder: European Commission (EC)
  • Project Code: 615307
  • Funding stream: FP7 | SP2 | ERC
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Other ORP type . 2017
Providers: NARCIS
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