A relaxed alternating CQ-algorithm for convex feasibility problems
Section snippets
Introduction and preliminaries
Due to their extraordinary utility and broad applicability in many areas of applied mathematics (most notably, fully-discretized models of problems in image reconstruction from projections, in image processing, and in intensity-modulated radiation therapy), algorithms for solving convex feasibility problems continue to receive great attention; see for instance [1], [2], [3], [4], [5] and also [6], [7], [8], [9]. In this paper our interest is in the study of the convergence of a relaxed
A weak convergence result
For sake of simplicity we set and remember that the Projection operator on a closed convex set of a Hilbert space admits the following useful characterization:
Given and , then if, and only if, and also has very attractive properties that make it particularly well suited for iterative algorithms. For instance, is firmly nonexpansive, namely for all see for instance Goebel and Reich [16].
Now, we are in a
Acknowledgments
I would like to thank N. Lehdili for his kind invitation to Jossigny and the two referees for their careful reading of the paper and for their pertinent comments and suggestions.
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