Algorithms for linear and convex feasibility problems: A brief study of iterative projection, localization and subgradient methods
Author(s)
Advisor
Akgül, MustafaDate
1998Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
224
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106
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Abstract
Several algorithms for the feasibility problem are investigated. For linear systems,
a number of different block projections approaches have been implemented and
compared. The parallel algorithm of Yang and Murty is observed to be much slower
than its sequential counterpart. Modification of the step size has allowed us to
obtain a much better algorithm, exhibiting considerable speedup when compared
to the sequential algorithm. For the convex feasibility problem an approach
combining rectangular cutting planes and subgradients is developed. Theoretical
convergence results are established for both ca^es. Two broad classes of image
recovery problems are formulated as linear feasibility problems and successfully
solved with the algorithms developed.
Keywords
Linear feasibilityregularization of ill conditioned problems
tomography
image reconstruction from projections
image restoration
image recovery
descent directions
analytic centers
central cutting (localization) methods
subgradient methods
sequential and parallel algorithms
long-step methods
constraints and block projections
surrogate
Cimmino’s method
the relaxation (successive orthogonal projections) method
projection methods
convex feasibility
Permalink
http://hdl.handle.net/11693/18555Collections
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