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Finite Convergence of a Subgradient Projections Method with Expanding Controls

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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.

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Author notes

  1. Wei Chen

    Present address: Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, MA, 02114, USA

Authors and Affiliations

  1. Department of Mathematics, University of Haifa, Mt. Carmel, Haifa, 31905, Israel

    Yair Censor

  2. Department of Computer Science, The Graduate Center, City University of New York, 365 Fifth Avenue, New York, NY, 10016, USA

    Wei Chen

  3. Department of Mathematics, Medgar Evers College, City University of New York, Brooklyn, New York, NY, 11225, USA

    Homeira Pajoohesh

Authors
  1. Yair Censor
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  2. Wei Chen
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  3. Homeira Pajoohesh
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Correspondence to Yair Censor.

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Censor, Y., Chen, W. & Pajoohesh, H. Finite Convergence of a Subgradient Projections Method with Expanding Controls. Appl Math Optim 64, 273–285 (2011). https://doi.org/10.1007/s00245-011-9139-8

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