A multiprojection algorithm using Bregman projections in a product space View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1994-09

AUTHORS

Yair Censor, Tommy Elfving

ABSTRACT

Generalized distances give rise to generalized projections into convex sets. An important question is whether or not one can use within the same projection algorithm different types of such generalized projections. This question has practical consequences in the area of signal detection and image recovery in situations that can be formulated mathematically as a convex feasibility problem. Using an extension of Pierra's product space formalism, we show here that a multiprojection algorithm converges. Our algorithm is fully simultaneous, i.e., it uses in each iterative stepall sets of the convex feasibility problem. Different multiprojection algorithms can be derived from our algorithmic scheme by a judicious choice of the Bregman functions which govern the process. As a by-product of our investigation we also obtain blockiterative schemes for certain kinds of linearly constraned optimization problems. More... »

PAGES

221-239

References to SciGraph publications

  • 1986-12. A relaxed version of Bregman's method for convex programming in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1989. Phase Retrieval and Zero Crossings in NONE
  • 1988-04. Parallel application of block-iterative methods in medical imaging and radiation therapy in MATHEMATICAL PROGRAMMING
  • 1980-03. Block-iterative methods for consistent and inconsistent linear equations in NUMERISCHE MATHEMATIK
  • 1992-06. Proximal minimization algorithm withD-functions in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1988-01. A successive projection method in MATHEMATICAL PROGRAMMING
  • 1981-07. An iterative row-action method for interval convex programming in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1991-05. On the convergence of Han's method for convex programming with quadratic objective in MATHEMATICAL PROGRAMMING
  • 1984-01. Decomposition through formalization in a product space in MATHEMATICAL PROGRAMMING
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    http://scigraph.springernature.com/pub.10.1007/bf02142692

    DOI

    http://dx.doi.org/10.1007/bf02142692

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