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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Viewing parallel projection methods as sequential ones in convex feasibility problems
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by G. Crombez PDF
Trans. Amer. Math. Soc. 347 (1995), 2575-2583 Request permission

Abstract:

We show that the parallel projection method with variable weights and one variable relaxation coefficient for obtaining a point in the intersection of a finite number of closed convex sets in a given Hilbert space may be interpreted as a semi-alternating sequential projection method in a suitably newly constructed Hilbert space. As such, convergence results for the parallel projection method may be derived from those which may be constructed in the semi-alternating sequential case.
References
    D. Butnariu and Y. Censor, On the behavior of a block-iterative projection method for solving convex feasibility problems, Internat. J. Computer Math. 43 (1990), 79-94.
  • G. Crombez, Weak and norm convergence of a parallel projection method in Hilbert spaces, Appl. Math. Comput. 56 (1993), no. 1, 35–48. MR 1216684, DOI 10.1016/0096-3003(93)90077-R
    • —, A parallel projection method based on sequential most remote set in convex feasibility problems (submitted for publication). A. R. De Pierro, An extended decomposition through formalization in product spaces, preprint. A. R. De Pierro and A. N. Iussem, A parallel projection method of finding a common point of a family of convex sets, Pesquisa Operacional 5 (1985), 1-20. L. G. Gubin, B. T. Polyak, and E. V. Raik, The method of projections for finding the common point of convex sets, USSR Comput. Math. and Math. Phys. 7 (1967), 1-24.
  • N. Ottavy, Strong convergence of projection-like methods in Hilbert spaces, J. Optim. Theory Appl. 56 (1988), no. 3, 433–461. MR 930217, DOI 10.1007/BF00939552
  • G. Pierra, Decomposition through formalization in a product space, Math. Programming 28 (1984), no. 1, 96–115. MR 727421, DOI 10.1007/BF02612715
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 2575-2583
  • MSC: Primary 65J05; Secondary 41A65, 65K99
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1277105-1
  • MathSciNet review: 1277105