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Analysis of the Projective Re-Normalization method on semidefinite programming feasibility problems

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dc.contributor.advisor Robert M. Freund. en_US
dc.contributor.author Yeung, Sai Hei en_US
dc.contributor.other Massachusetts Institute of Technology. Computation for Design and Optimization Program. en_US
dc.date.accessioned 2008-12-11T18:29:36Z
dc.date.available 2008-12-11T18:29:36Z
dc.date.copyright 2008 en_US
dc.date.issued 2008 en_US
dc.identifier.uri http://hdl.handle.net/1721.1/43800
dc.description Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. en_US
dc.description Includes bibliographical references (p. 75-76). en_US
dc.description.abstract In this thesis, we study the Projective Re-Normalization method (PRM) for semidefinite programming feasibility problems. To compute a good normalizer for PRM, we propose and study the advantages and disadvantages of a Hit & Run random walk with Dikin ball dilation. We perform this procedure on an ill-conditioned two dimensional simplex to show the Dikin ball Hit & Run random walk mixes much faster than standard Hit & Run random walk. In the last part of this thesis, we conduct computational testing of the PRM on a set of problems from the SDPLIB [3] library derived from control theory and several univariate polynomial problems sum of squares (SOS) problems. Our results reveal that our PRM implementation is effective for problems of smaller dimensions but tends to be ineffective (or even detrimental) for problems of larger dimensions. en_US
dc.description.statementofresponsibility by Sai Hei Yeung. en_US
dc.format.extent 76 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.rights.uri http://dspace.mit.edu/handle/1721.1/7582 en_US
dc.subject Computation for Design and Optimization Program. en_US
dc.title Analysis of the Projective Re-Normalization method on semidefinite programming feasibility problems en_US
dc.title.alternative Projective Re-Normalization method on semidefinite programming feasibility problems en_US
dc.type Thesis en_US
dc.description.degree S.M. en_US
dc.contributor.department Massachusetts Institute of Technology. Computation for Design and Optimization Program. en_US
dc.identifier.oclc 261488559 en_US


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