A sequential iteration algorithm with non-monotoneous behaviour in the method of projections onto convex sets

Title:

A sequential iteration algorithm with non-monotoneous behaviour in the method of projections onto convex sets

Creator:

Crombez, Gilbert

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:5018db77-8ab1-4298-b348-6a37a5d5929d
uuid:5018db77-8ab1-4298-b348-6a37a5d5929d

Subject:

projections onto convex sets, nonlinear operators, and slow convergence

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

491-506

Source:

Czechoslovak Mathematical Journal | 2006 Volume:56 | Number:2

Harvested from:

CDK

Metadata only:

false