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Zbl 0828.65065
Censor, Yair; Elfving, Tommy
A multiprojection algorithm using Bregman projections in a product space. (English)
[J] Numer. Algorithms 8, No.2-4, 221-239 (1994). ISSN 1017-1398; ISSN 1572-9265/e

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.\par Using an extension of Pierra's product space formalism, it is shown that a multiprojection algorithm converges. The algorithm is fully simultaneous, i.e., it uses all sets of the convex feasibility problem in each iterative step. Different multiprojection algorithms can be derived from this algorithmic scheme by a judicious choice of the Bregman functions that govern the process.\par As a by-product of the investigation, the authors obtain block-iterative schemes for certain kinds of linearly constrained optimization problems.
[J.Guddat (Berlin)]

MSC 2000:: *65K05 Mathematical programming (numerical methods)
90C30 Nonlinear programming

Keywords: convergence; signal detection; image recovery; convex feasibility problem; Pierra's product space; multiprojection algorithm; Bregman functions; block-iterative schemes; linearly constrained optimization

Cited in: Zbl 1200.49034 Zbl 0940.65072

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