A dual approach to constrained interpolation from a convex subset of Hilbert space
Journal of Approximation Theory
Parallel Optimization: Theory, Algorithms and Applications
Parallel Optimization: Theory, Algorithms and Applications
Projection algorithms and monotone operators
Projection algorithms and monotone operators
The rate of convergence for the cyclic projections algorithm I: angles between convex sets
Journal of Approximation Theory
The rate of convergence for the cyclic projections algorithm II: norms of nonlinear operators
Journal of Approximation Theory
Functions with prescribed best linear approximations
Journal of Approximation Theory
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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.