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Iterative algorithms with seminorm-induced oblique projections

Yair Censor (yair***at***math.haifa.ac.il)
Tommy Elfving (toelf***at***mai.liu.se)

Abstract: A definition of oblique projections onto closed convex sets that use seminorms induced by diagonal matrices which may have zeros on the diagonal is introduced. Existence and uniqueness of such projections are secured via directional affinity of the sets with respect to the diagonal matrices involved. A block-iterative algorithmic scheme for solving the convex feasibility problem, employing seminorm-induced oblique projections, is constructed and its convergence for the consistent case is established. The fully simultaneous algorithm converges also in the inconsistent case to the minimum of a certain proximity function.

Keywords: Seminorm, oblique projections, Block-iterative algorithm, proximity function.

Category 1: Nonlinear Optimization

Category 2: Convex and Nonsmooth Optimization

Citation: Abstract and Applied Analysis, Vol. 7 (2003), pp. 387-406.

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Entry Submitted: 12/10/2002
Entry Accepted: 12/10/2002
Entry Last Modified: 06/16/2003

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