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Volume 10 (2014) Article 11 pp. 257-295
Efficient Rounding for the Noncommutative Grothendieck Inequality
Received: February 16, 2013
Revised: August 11, 2014
Published: October 2, 2014
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Keywords: approximation algorithms, Grothendieck inequality, semidefinite programming, principal component analysis
ACM Classification: G.1.6
AMS Classification: 68W25

Abstract: [Plain Text Version]

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.