Abstract
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.
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Crombez, G. A sequential iteration algorithm with non-monotoneous behaviour in the method of projections onto convex sets. Czech Math J 56, 491–506 (2006). https://doi.org/10.1007/s10587-006-0031-7
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DOI: https://doi.org/10.1007/s10587-006-0031-7