### Abstract

We consider a successive projection method for finding a common point in the intersection of closed convex sets with a nonempty interior. We first generalize an iterative projection algorithm known as acceleration method that was introduced earlier in [1] from the case of two closed convex sets to a finite number of closed convex sets, assuming that the intersection set has a nonempty interior. In particular, we establish the convergence of such an algorithm to a common feasible point in the intersection of all the sets. Following this, we establish a geometric rate of convergence for the generalized method when we restrict the convex sets to the class of half-spaces in finite dimensional Euclidean spaces.

Original language | English (US) |
---|---|

Title of host publication | 2016 American Control Conference, ACC 2016 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 4422-4427 |

Number of pages | 6 |

Volume | 2016-July |

ISBN (Electronic) | 9781467386821 |

DOIs | |

State | Published - Jul 28 2016 |

Externally published | Yes |

Event | 2016 American Control Conference, ACC 2016 - Boston, United States Duration: Jul 6 2016 → Jul 8 2016 |

### Other

Other | 2016 American Control Conference, ACC 2016 |
---|---|

Country | United States |

City | Boston |

Period | 7/6/16 → 7/8/16 |

### Keywords

- Acceleration method
- Closed convex sets
- Convergence rate
- Half-spaces
- Successive projection

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

## Cite this

*2016 American Control Conference, ACC 2016*(Vol. 2016-July, pp. 4422-4427). [7525618] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACC.2016.7525618