### 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 |

### Other

Other | 45th Annual ACM Symposium on Theory of Computing, STOC 2013 |
---|---|

Country | United States |

City | Palo Alto, CA |

Period | 6/1/13 → 6/4/13 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Software

### Cite this

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

**Efficient rounding for the noncommutative grothendieck inequality.** / Naor, Assaf; Regev, Oded; Vidick, Thomas.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing.*pp. 71-80, 45th Annual ACM Symposium on Theory of Computing, STOC 2013, Palo Alto, CA, United States, 6/1/13. https://doi.org/10.1145/2488608.2488618

}

TY - GEN

T1 - Efficient rounding for the noncommutative grothendieck inequality

AU - Naor, Assaf

AU - Regev, Oded

AU - Vidick, Thomas

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Grothendieck inequality

KW - Principal component analysis

KW - Rounding algorithm

KW - Semidefinite programming

UR - http://www.scopus.com/inward/record.url?scp=84879833771&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84879833771&partnerID=8YFLogxK

U2 - 10.1145/2488608.2488618

DO - 10.1145/2488608.2488618

M3 - Conference contribution

AN - SCOPUS:84879833771

SN - 9781450320290

SP - 71

EP - 80

BT - STOC 2013 - Proceedings of the 2013 ACM Symposium on Theory of Computing

ER -