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A multiprojection algorithm using Bregman projections in a product space

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.

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Communicated by C. Brezinski

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Censor, Y., Elfving, T. A multiprojection algorithm using Bregman projections in a product space. Numer Algor 8, 221–239 (1994). https://doi.org/10.1007/BF02142692

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  • DOI: https://doi.org/10.1007/BF02142692

Keywords

  • Non-orthogonal projections
  • convex feasibility problem
  • bregman's generalized distance

Subject classification

  • 90 C25
  • 90 C30