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

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buir.advisorAkgül, Mustafa
dc.contributor.authorÖzaktaş, Hakan
dc.date.accessioned2016-01-08T20:20:22Z
dc.date.available2016-01-08T20:20:22Z
dc.date.issued1998
dc.descriptionAnkara : Department of Industrial Engineering and Institute of Engineering and Sciences, Bilkent Univ., 1998.en_US
dc.descriptionThesis (Ph.D.) -- Bilkent University, 1998.en_US
dc.descriptionIncludes bibliographical references leaves 86-93.en_US
dc.description.abstractSeveral 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.en_US
dc.description.provenanceMade available in DSpace on 2016-01-08T20:20:22Z (GMT). No. of bitstreams: 1 1.pdf: 78510 bytes, checksum: d85492f20c2362aa2bcf4aad49380397 (MD5)en
dc.description.statementofresponsibilityÖzaktaş, Hakanen_US
dc.format.extentxi, 94 leavesen_US
dc.identifier.urihttp://hdl.handle.net/11693/18555
dc.language.isoEnglishen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectLinear feasibilityen_US
dc.subjectregularization of ill conditioned problemsen_US
dc.subjecttomographyen_US
dc.subjectimage reconstruction from projectionsen_US
dc.subjectimage restorationen_US
dc.subjectimage recoveryen_US
dc.subjectdescent directionsen_US
dc.subjectanalytic centersen_US
dc.subjectcentral cutting (localization) methodsen_US
dc.subjectsubgradient methodsen_US
dc.subjectsequential and parallel algorithmsen_US
dc.subjectlong-step methodsen_US
dc.subjectconstraints and block projectionsen_US
dc.subjectsurrogateen_US
dc.subjectCimmino’s methoden_US
dc.subjectthe relaxation (successive orthogonal projections) methoden_US
dc.subjectprojection methodsen_US
dc.subjectconvex feasibilityen_US
dc.subject.lccT57.74 .O93 1998en_US
dc.subject.lcshLinear programming.en_US
dc.subject.lcshConvex programming.en_US
dc.subject.lcshRelaxation methods (Mathematics).en_US
dc.titleAlgorithms for linear and convex feasibility problems: A brief study of iterative projection, localization and subgradient methodsen_US
dc.typeThesisen_US
thesis.degree.disciplineIndustrial Engineering
thesis.degree.grantorBilkent University
thesis.degree.levelDoctoral
thesis.degree.namePh.D. (Doctor of Philosophy)

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