The rate of convergence for the cyclic projections algorithm III: Regularity of convex sets

23Citations
Citations of this article
13Readers
Mendeley users who have this article in their library.

Abstract

The cyclic projections algorithm is an important method for determining a point in the intersection of a finite number of closed convex sets in a Hilbert space. That is, for determining a solution to the "convex feasibility" problem. This is the third paper in a series on a study of the rate of convergence for the cyclic projections algorithm. In the first of these papers, we showed that the rate could be described in terms of the "angles" between the convex sets involved. In the second, we showed that these angles often had a more tractable formulation in terms of the "norm" of the product of the (nonlinear) metric projections onto related convex sets. In this paper, we show that the rate of convergence of the cyclic projections algorithm is also intimately related to the "linear regularity property" of Bauschke and Borwein, the "normal property" of Jameson (as well as Bakan, Deutsch, and Li's generalization of Jameson's normal property), the "strong conical hull intersection property" of Deutsch, Li, and Ward, and the rate of convergence of iterated parallel projections. Such properties have already been shown to be important in various other contexts as well. © 2008 Elsevier Inc. All rights reserved.

Cite

CITATION STYLE

APA

Deutsch, F., & Hundal, H. (2008). The rate of convergence for the cyclic projections algorithm III: Regularity of convex sets. Journal of Approximation Theory, 155(2), 155–184. https://doi.org/10.1016/j.jat.2008.04.001

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free