2019-01-31
Lower bounds on matrix factorization ranks via noncommutative polynomial optimization
Publication
Publication
Foundations of Computational Mathematics , Volume 19 p. 1013- 1070
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 analogs: the completely positive rank and the completely positive semidefinite rank. We study convergence properties of our hierarchies, compare them extensively to known lower bounds, and provide some (numerical) examples.
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| , , , , , | |
| doi.org/10.1007/s10208-018-09410-y | |
| Foundations of Computational Mathematics | |
| Approximation Algorithms, Quantum Information and Semidefinite Optimization , Progress in quantum computing:Algorithms, communication, and applications | |
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| Organisation | Networks and Optimization |
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Gribling, S., de Laat, D., & Laurent, M. (2019). Lower bounds on matrix factorization ranks via noncommutative polynomial optimization. Foundations of Computational Mathematics, 19, 1013–1070. doi:10.1007/s10208-018-09410-y |
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