Title: | Non-monotoneous parallel iteration for solving convex feasibility problems (English) |

Author: | Crombez, Gilbert |

Language: | English |

Journal: | Kybernetika |

ISSN: | 0023-5954 |

Volume: | 39 |

Issue: | 5 |

Year: | 2003 |

Pages: | [547]-560 |

Summary lang: | English |

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Category: | math |

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Summary: | The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in an Euclidean space, sometimes leads to slow convergence of the constructed sequence. Such slow convergence depends both on the choice of the starting point and on the monotoneous behaviour of the usual algorithms. As there is normally no indication of how to choose the starting point in order to avoid slow convergence, we present in this paper a non-monotoneous parallel algorithm that may eliminate considerably the influence of the starting point. (English) |

Keyword: | inherently parallel methods |

Keyword: | convex feasibility problems |

Keyword: | projections onto convex sets |

Keyword: | slow convergence |

MSC: | 47H09 |

MSC: | 47J25 |

MSC: | 65B99 |

MSC: | 65D18 |

MSC: | 65K05 |

MSC: | 65Y05 |

MSC: | 90C25 |

idZBL: | Zbl 1249.65040 |

idMR: | MR2042340 |

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Date available: | 2009-09-24T19:56:37Z |

Last updated: | 2015-03-24 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/135554 |

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Reference: | [6] Crombez G.: Viewing parallel projection methods as sequential ones in convex feasibility problems.Trans. Amer. Math. Soc. 347 (1995), 2575–2583 Zbl 0846.46010, MR 1277105, 10.1090/S0002-9947-1995-1277105-1 |

Reference: | [7] Crombez G.: Solving convex feasibility problems by a parallel projection method with geometrically defined parameters.Appl. Anal. 64 (1997), 277–290 Zbl 0877.65033, MR 1460084, 10.1080/00036819708840536 |

Reference: | [8] Crombez G.: Improving the speed of convergence in the method of projections onto convex sets.Publ. Math. Debrecen 58 (2001), 29–48 Zbl 0973.65001, MR 1807574 |

Reference: | [9] Gubin L. G., Polyak B. T., Raik E. V.: The method of projections for finding the common point of convex sets.U.S.S.R. Comput. Math. and Math. Phys. 7 (1967), 1–24 10.1016/0041-5553(67)90113-9 |

Reference: | [10] Kiwiel K.: Block-iterative surrogate projection methods for convex feasibility problems.Linear Algebra Appl. 215 (1995), 225–259 Zbl 0821.65037, MR 1317480 |

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Reference: | [12] Stark H., Yang Y.: Vector Space Projections.Wiley, New York 1998 Zbl 0903.65001 |

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