Homogenization of Mixed Horizontal LCPs and Applications

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dc.contributor.advisorPotra, Florian A
dc.contributor.authorPetra, Cosmin G.
dc.contributor.departmentMathematics and Statistics
dc.contributor.programMathematics, Applied
dc.date.accessioned2015-10-14T03:11:41Z
dc.date.available2015-10-14T03:11:41Z
dc.date.issued2009-01-01
dc.description.abstractIn optimization, a homogeneous model is an artificial transformation of a given problem. The transformation is done such that the homogeneous problem has always a solution even if the original problem does not. Moreover, without having any assumption on the feasibility of the original problem, the homogeneous model is able to provide the solution if it exists, or a certificate of infeasibility otherwise. The first part of the thesis will introduce a homogeneous model for mixed linear complementarity problems which represent a generalization of the standard linear complementarity problems. We also study the properties of the model and show that the interior-point methods can be efficiently used for the numerical solutions of the homogenous problem. The second part of the thesis is concerned with a computational study on the use of an optimization-based method in the simulation of fuel motion in a pebble bed reactor. The performance of several optimization packages (BLMVM, TRON, OOQP, and Mosek) for quadratic problems needed to simulate the system is investigated and reported. OOQP will be presented with both the default solver MA27 and our implementation based on CHOLMOD. CHOLMOD-based OOQP version is the fastest of all the packages tested. It consistently uses only about three times more memory than BLMVM, while achieving far higher precision levels. Both solvers behave predictably with the number of pebbles and can be used as robust software solutions in the simulation of the pebble bed reactor.
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dc.genredissertations
dc.identifierdoi:10.13016/M2R68K
dc.identifier.other10163
dc.identifier.urihttp://hdl.handle.net/11603/1014
dc.languageen
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Theses and Dissertations Collection
dc.relation.ispartofUMBC Graduate School Collection
dc.relation.ispartofUMBC Student Collection
dc.relation.ispartofUMBC Mathematics and Statistics Department Collection
dc.rightsThis item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu.
dc.sourceOriginal File Name: Petra_umbc_0434D_10163.pdf
dc.subjectcomplementarity
dc.subjecthomogenization
dc.subjectinterior-point method
dc.subjectlcp
dc.subjectnonlinear optimization
dc.subjectnumerical methods
dc.titleHomogenization of Mixed Horizontal LCPs and Applications
dc.typeText
dcterms.accessRightsAccess limited to the UMBC community. Item may possibly be obtained via Interlibrary Loan through a local library, pending author/copyright holder's permission.

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