Algorithms for linear and convex feasibility problems: A brief study of iterative projection, localization and subgradient methods

Date
1998
Advisor
Akgül, Mustafa
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Bilkent University
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Language
English
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Thesis
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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.

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Linear feasibility, regularization 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
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Published Version (Please cite this version)