caa a22 4500 445842202 CHVBK 20180317145348.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00245-011-9139-8 doi (NATIONALLICENCE)springer-10.1007/s00245-011-9139-8 Finite Convergence of a Subgradient Projections Method with Expanding Controls [Elektronische Daten] [Yair Censor, Wei Chen, Homeira Pajoohesh] 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. Springer Science+Business Media, LLC, 2011 Convex feasibility problem nationallicence Modified subgradient projections nationallicence Finite convergence nationallicence Expanding controls nationallicence Repetitive control nationallicence Quasi-cyclic control nationallicence Censor Yair Department of Mathematics, University of Haifa, Mt. Carmel, 31905, Haifa, Israel aut Chen Wei Department of Computer Science, The Graduate Center, City University of New York, 365 Fifth Avenue, 10016, New York, NY, USA aut Pajoohesh Homeira Department of Mathematics, Medgar Evers College, City University of New York, Brooklyn, 11225, New York, NY, USA aut Applied Mathematics & Optimization Springer-Verlag 64/2(2011-10-01), 273-285 0095-4616 64:2<273 2011 64 245 https://doi.org/10.1007/s00245-011-9139-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00245-011-9139-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Censor Yair Department of Mathematics, University of Haifa, Mt. Carmel, 31905, Haifa, Israel aut NATIONALLICENCE 700 1- Chen Wei Department of Computer Science, The Graduate Center, City University of New York, 365 Fifth Avenue, 10016, New York, NY, USA aut NATIONALLICENCE 700 1- Pajoohesh Homeira Department of Mathematics, Medgar Evers College, City University of New York, Brooklyn, 11225, New York, NY, USA aut NATIONALLICENCE 773 0- Applied Mathematics & Optimization Springer-Verlag 64/2(2011-10-01), 273-285 0095-4616 64:2<273 2011 64 245 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer