## Abstract

Consider the problem of minimizing the sum of a smooth (possibly non-convex) and a convex (possibly nonsmooth) function involving a large number of variables. A popular approach to solve this problem is the block coordinate descent (BCD) method whereby at each iteration only one variable block is updated while the remaining variables are held fixed. With the recent advances in the developments of the multi-core parallel processing technology, it is desirable to parallelize the BCD method by allowing multiple blocks to be updated simultaneously at each iteration of the algorithm. In this work, we propose an inexact parallel BCD approach where at each iteration, a subset of the variables is updated in parallel by minimizing convex approximations of the original objective function. We investigate the convergence of this parallel BCD method for both randomized and cyclic variable selection rules. We analyze the asymptotic and non-asymptotic convergence behavior of the algorithm for both convex and non-convex objective functions. The numerical experiments suggest that for a special case of Lasso minimization problem, the cyclic block selection rule can outperform the randomized rule.

Original language | English (US) |
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Title of host publication | Advances in Neural Information Processing Systems |

Publisher | Neural information processing systems foundation |

Pages | 1440-1448 |

Number of pages | 9 |

Volume | 2 |

Edition | January |

State | Published - 2014 |

Event | 28th Annual Conference on Neural Information Processing Systems 2014, NIPS 2014 - Montreal, Canada Duration: Dec 8 2014 → Dec 13 2014 |

### Other

Other | 28th Annual Conference on Neural Information Processing Systems 2014, NIPS 2014 |
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Country | Canada |

City | Montreal |

Period | 12/8/14 → 12/13/14 |