×

Solving convex feasibility problems by a parallel projection method with geometrically-defined parameters. (English) Zbl 0877.65033

The parallel projection method to find, in an iterative manner, a point in the nonempty intersection of a finite number of closed convex sets in a real Hilbert space, uses at each iteration step a number of nonnegative weights and a positive relaxation coefficient; they may vary at each step, but should be chosen such that the resulting sequence is (at least weakly) convergent to a point in the intersection. We present a method to determine these variable quantities at each step by geometrical conditions in an associated Hilbert space.
Reviewer: G.Crombez (Gent)

MSC:

65J05 General theory of numerical analysis in abstract spaces
46C99 Inner product spaces and their generalizations, Hilbert spaces
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1016/0024-3795(89)90375-3 · Zbl 0679.65046 · doi:10.1016/0024-3795(89)90375-3
[2] DOI: 10.1080/00207169008803865 · Zbl 0708.90064 · doi:10.1080/00207169008803865
[3] DOI: 10.1016/0096-3003(93)90077-R · Zbl 0783.65049 · doi:10.1016/0096-3003(93)90077-R
[4] DOI: 10.2307/2154839 · Zbl 0846.46010 · doi:10.2307/2154839
[5] DOI: 10.1016/0041-5553(67)90113-9 · Zbl 0199.51002 · doi:10.1016/0041-5553(67)90113-9
[6] DOI: 10.1007/BF01389537 · Zbl 0571.65051 · doi:10.1007/BF01389537
[7] Levi A., In:Image Recovery: Theory and Application pp 277– (1987)
[8] DOI: 10.1007/BF02612715 · Zbl 0523.49022 · doi:10.1007/BF02612715
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.