Geodesic
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.

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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.
Classification : 40A99, 47H09, 47H10, 47N10, 49M30, 52A20, 90C25
Keywords: projections onto convex sets; nonlinear operators; slow convergence 
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     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},
     publisher = {mathdoc},
     volume = {56},
     number = {2},
     year = {2006},
     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/