A multiprojection algorithm using Bregman projections in a product space

Yair Censor, Tommy Elfving

Research output: Contribution to journalArticlepeer-review

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 step all 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.

Original languageEnglish
Pages (from-to)221-239
Number of pages19
JournalNumerical Algorithms
Volume8
Issue number2
DOIs
StatePublished - Sep 1994

Keywords

  • bregman's generalized distance
  • convex feasibility problem
  • Non-orthogonal projections
  • Subject classification: 90C25, 90C30

ASJC Scopus subject areas

  • Applied Mathematics

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