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A sequential iteration algorithm with non-monotoneous behaviour in the method of projections onto convex sets
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 491-506 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 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.
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.
Classification : 40A99, 47H09, 47H10, 47N10, 49M30, 52A20, 90C25
Keywords: projections onto convex sets; nonlinear operators; slow convergence 
@article{CMJ_2006_56_2_a14,
     author = {Crombez, G.},
     title = {A sequential iteration algorithm with non-monotoneous behaviour in the method of projections onto convex sets},
     journal = {Czechoslovak Mathematical Journal},
     pages = {491--506},
     year = {2006},
     volume = {56},
     number = {2},
     mrnumber = {2291750},
     zbl = {1164.47399},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2006_56_2_a14/}
}
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Crombez, G. A sequential iteration algorithm with non-monotoneous behaviour in the method of projections onto convex sets. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 2, pp. 491-506. http://geodesic.mathdoc.fr/item/CMJ_2006_56_2_a14/