Publication Date:
2011-06-11
Description:
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. Content Type Journal Article Pages 1-13 DOI 10.1007/s00245-011-9139-8 Authors Yair Censor, Department of Mathematics, University of Haifa, Mt. Carmel, Haifa, 31905 Israel Wei Chen, Department of Computer Science, The Graduate Center, City University of New York, 365 Fifth Avenue, New York, NY 10016, USA Homeira Pajoohesh, Department of Mathematics, Medgar Evers College, City University of New York, Brooklyn, New York, NY 11225, USA Journal Applied Mathematics & Optimization Online ISSN 1432-0606 Print ISSN 0095-4616
Print ISSN:
0095-4616
Electronic ISSN:
1432-0606
Topics:
Mathematics
