Hilbertian convex feasibility problem: Convergence of projection methods

Hilbertian convex feasibility problem: Convergence of projection methods The classical problem of finding a point in the intersection of countably many closed and convex sets in a Hilbert space is considered. Extrapolated iterations of convex combinations of approximate projections onto subfamilies of sets are investigated to solve this problem. General hypotheses are made on the regularity of the sets and various strategies are considered to control the order in which the sets are selected. Weak and strong convergence results are established within thisbroad framework, which provides a unified view of projection methods for solving hilbertian convex feasibility problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Hilbertian convex feasibility problem: Convergence of projection methods

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Publisher
Springer-Verlag
Copyright
Copyright © 1997 by Springer-Verlag New York Inc.
Subject
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/BF02683333
Publisher site
See Article on Publisher Site

Abstract

The classical problem of finding a point in the intersection of countably many closed and convex sets in a Hilbert space is considered. Extrapolated iterations of convex combinations of approximate projections onto subfamilies of sets are investigated to solve this problem. General hypotheses are made on the regularity of the sets and various strategies are considered to control the order in which the sets are selected. Weak and strong convergence results are established within thisbroad framework, which provides a unified view of projection methods for solving hilbertian convex feasibility problems.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: May 1, 1997

References

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