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dc.contributor.authorSteffy, Daniel E.en_US
dc.date.accessioned2011-07-06T16:49:04Z
dc.date.available2011-07-06T16:49:04Z
dc.date.issued2011-01-24en_US
dc.identifier.urihttp://hdl.handle.net/1853/39639
dc.description.abstractThe focus of this dissertation is the advancement of theory and computation related to exact precision mathematical programming. Optimization software based on floating-point arithmetic can return suboptimal or incorrect resulting because of round-off errors or the use of numerical tolerances. Exact or correct results are necessary for some applications. Implementing software entirely in rational arithmetic can be prohibitively slow. A viable alternative is the use of hybrid methods that use fast numerical computation to obtain approximate results that are then verified or corrected with safe or exact computation. We study fast methods for sparse exact rational linear algebra, which arises as a bottleneck when solving linear programming problems exactly. Output sensitive methods for exact linear algebra are studied. Finally, a new method for computing valid linear programming bounds is introduced and proven effective as a subroutine for solving mixed-integer linear programming problems exactly. Extensive computational results are presented for each topic.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectLinear programmingen_US
dc.subjectMixed-integer programmingen_US
dc.subjectExact computationen_US
dc.subjectSymbolic computationen_US
dc.subjectLinear algebraen_US
dc.subject.lcshProgramming (Mathematics)
dc.subject.lcshMathematical optimization
dc.subject.lcshLinear programming
dc.titleTopics in exact precision mathematical programmingen_US
dc.typeDissertationen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentAlgorithms, Combinatorics, and Optimizationen_US
dc.description.advisorCommittee Chair: Dr. William J. Cook; Committee Member: Dr. George Nemhauser; Committee Member: Dr. Robin Thomas; Committee Member: Dr. Santanu Dey; Committee Member: Dr. Shabbir Ahmed; Committee Member: Dr. Zonghao Guen_US


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