Finite Convergence of a Subgradient Projections Method with Expanding Controls

Finite Convergence of a Subgradient Projections Method with Expanding Controls We study finite convergence of the modified cyclic subgradient projections (MCSP) algorithm for the convex feasibility problem (CFP) in the Euclidean space. Expanding control sequences allow the indices of the sets of the CFP to re-appear and be used again by the algorithm within windows of iteration indices whose lengths are not constant but may increase without bound. Motivated by another development in finitely convergent sequential algorithms that has a significant real-world application in the field of radiation therapy treatment planning, we show that the MCSP algorithm retains its finite convergence when used with an expanding control that is repetitive and fulfills an additional condition. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Finite Convergence of a Subgradient Projections Method with Expanding Controls

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Publisher
Springer-Verlag
Copyright
Copyright © 2011 by Springer Science+Business Media, LLC
Subject
Mathematics; Mathematical Methods in Physics; Theoretical, Mathematical and Computational Physics; Calculus of Variations and Optimal Control; Optimization; Numerical and Computational Physics; Systems Theory, Control
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-011-9139-8
Publisher site
See Article on Publisher Site

Abstract

We study finite convergence of the modified cyclic subgradient projections (MCSP) algorithm for the convex feasibility problem (CFP) in the Euclidean space. Expanding control sequences allow the indices of the sets of the CFP to re-appear and be used again by the algorithm within windows of iteration indices whose lengths are not constant but may increase without bound. Motivated by another development in finitely convergent sequential algorithms that has a significant real-world application in the field of radiation therapy treatment planning, we show that the MCSP algorithm retains its finite convergence when used with an expanding control that is repetitive and fulfills an additional condition.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2011

References

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