### 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 constant-factor polynomial time 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 principle component analysis and the orthogonal Procrustes problem.

Original language | English (US) |
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Title of host publication | STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing |

Pages | 71-80 |

Number of pages | 10 |

DOIs | |

State | Published - 2013 |

Event | 45th Annual ACM Symposium on Theory of Computing, STOC 2013 - Palo Alto, CA, United States Duration: Jun 1 2013 → Jun 4 2013 |

### Publication series

Name | Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN (Print) | 0737-8017 |

### Other

Other | 45th Annual ACM Symposium on Theory of Computing, STOC 2013 |
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Country | United States |

City | Palo Alto, CA |

Period | 6/1/13 → 6/4/13 |

### All Science Journal Classification (ASJC) codes

- Software

### Keywords

- Grothendieck inequality
- Principal component analysis
- Rounding algorithm
- Semidefinite programming

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## Cite this

*STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing*(pp. 71-80). (Proceedings of the Annual ACM Symposium on Theory of Computing). https://doi.org/10.1145/2488608.2488618