Non-monotoneous parallel iteration for solving convex feasibility problems

Gilbert Crombez

Kybernetika (2003)

  • Volume: 39, Issue: 5, page [547]-560
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Crombez, Gilbert. "Non-monotoneous parallel iteration for solving convex feasibility problems." Kybernetika 39.5 (2003): [547]-560. <http://eudml.org/doc/33664>.

@article{Crombez2003,
abstract = {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.},
author = {Crombez, Gilbert},
journal = {Kybernetika},
keywords = {inherently parallel methods; convex feasibility problems; projections onto convex sets; slow convergence; inherently parallel method; convex feasibility problem; projections onto convex set; slow convergence; algorithms},
language = {eng},
number = {5},
pages = {[547]-560},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Non-monotoneous parallel iteration for solving convex feasibility problems},
url = {http://eudml.org/doc/33664},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Crombez, Gilbert
TI - Non-monotoneous parallel iteration for solving convex feasibility problems
JO - Kybernetika
PY - 2003
PB - Institute of Information Theory and Automation AS CR
VL - 39
IS - 5
SP - [547]
EP - 560
AB - 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.
LA - eng
KW - inherently parallel methods; convex feasibility problems; projections onto convex sets; slow convergence; inherently parallel method; convex feasibility problem; projections onto convex set; slow convergence; algorithms
UR - http://eudml.org/doc/33664
ER -

References

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  7. Crombez G., 10.1080/00036819708840536, Appl. Anal. 64 (1997), 277–290 (1997) Zbl0877.65033MR1460084DOI10.1080/00036819708840536
  8. Crombez G., Improving the speed of convergence in the method of projections onto convex sets, Publ. Math. Debrecen 58 (2001), 29–48 Zbl0973.65001MR1807574
  9. Gubin L. G., Polyak B. T., Raik E. V., 10.1016/0041-5553(67)90113-9, U.S.S.R. Comput. Math. and Math. Phys. 7 (1967), 1–24 (1967) DOI10.1016/0041-5553(67)90113-9
  10. Kiwiel K., Block-iterative surrogate projection methods for convex feasibility problems, Linear Algebra Appl. 215 (1995), 225–259 (1995) Zbl0821.65037MR1317480
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  12. Stark H., Yang Y., Vector Space Projections, Wiley, New York 1998 Zbl0903.65001

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