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      • Dept. of Industrial Engineering - Ph.D. / Sc.D.
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      • Theses - Department of Industrial Engineering
      • Dept. of Industrial Engineering - Ph.D. / Sc.D.
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      Algorithms for linear and convex feasibility problems: A brief study of iterative projection, localization and subgradient methods

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      Author(s)
      Özaktaş, Hakan
      Advisor
      Akgül, Mustafa
      Date
      1998
      Publisher
      Bilkent University
      Language
      English
      Type
      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.
      Keywords
      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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      http://hdl.handle.net/11693/18555
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