| Title:
|
A sequential iteration algorithm with non-monotoneous behaviour in the method of projections onto convex sets (English) |
| Author:
|
Crombez, G. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
491-506 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in a Euclidean space, may lead to slow convergence of the constructed sequence when that sequence enters some narrow “corridor” between two or more convex sets. A way to leave such corridor consists in taking a big step at different moments during the iteration, because in that way the monotoneous behaviour that is responsible for the slow convergence may be interrupted. In this paper we present a technique that may introduce interruption of the monotony for a sequential algorithm, but that at the same time guarantees convergence of the constructed sequence to a point in the intersection of the sets. We compare experimentally the behaviour concerning the speed of convergence of the new algorithm with that of an existing monotoneous algorithm. (English) |
| Keyword:
|
projections onto convex sets |
| Keyword:
|
nonlinear operators |
| Keyword:
|
slow convergence |
| MSC:
|
40A99 |
| MSC:
|
47H09 |
| MSC:
|
47H10 |
| MSC:
|
47N10 |
| MSC:
|
49M30 |
| MSC:
|
52A20 |
| MSC:
|
90C25 |
| idZBL:
|
Zbl 1164.47399 |
| idMR:
|
MR2291750 |
| . |
| Date available:
|
2009-09-24T11:34:47Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128080 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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