### Abstract

The classical Grothendieck inequality has applications to the design of approximation algorithms for NP-hard optimization problems. We show that an algorithmic interpretation may also be given for a noncommutative generalization of the Grothendieck inequality due to Pisier and Haagerup. Our main result, an efficient rounding procedure for this inequality, leads to a polynomial-time constant-factor approximation algorithm for an optimization problem which generalizes the Cut Norm problem of Frieze and Kannan, and is shown here to have additional applications to robust principal component analysis and the orthogonal Procrustes problem.

Original language | English (US) |
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Pages (from-to) | 257-295 |

Number of pages | 39 |

Journal | Theory of Computing |

Volume | 10 |

DOIs | |

State | Published - Oct 2 2014 |

### Keywords

- Approximation algorithms
- Grothendieck inequality
- Principal component analysis
- Semidefinite programming

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computational Theory and Mathematics

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## Cite this

Naor, A., Regev, O., & Vidick, T. (2014). Efficient rounding for the noncommutative grothendieck inequality.

*Theory of Computing*,*10*, 257-295. https://doi.org/10.4086/toc.2014.v010a011