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Computational issues and related mathematics of an exponential annealing homotropy for conic optimization

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dc.contributor.advisor Robert M. Freund. en_US
dc.contributor.author Chen, Jeremy, S.M. Massachusetts Institute of Technology en_US
dc.contributor.other Massachusetts Institute of Technology. Computation for Design and Optimization Program. en_US
dc.date.accessioned 2008-05-19T16:13:22Z
dc.date.available 2008-05-19T16:13:22Z
dc.date.copyright 2007 en_US
dc.date.issued 2007 en_US
dc.identifier.uri http://hdl.handle.net/1721.1/41737
dc.description Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2007. en_US
dc.description Includes bibliographical references (p. 105-106). en_US
dc.description.abstract We present a further study and analysis of an exponential annealing based algorithm for convex optimization. We begin by developing a general framework for applying exponential annealing to conic optimization. We analyze the hit-and-run random walk from the perspective of convergence and develop (partially) an intuitive picture that views it as the limit of a sequence of finite state Markov chains. We then establish useful results that guide our sampling. Modifications are proposed that seek to raise the computational practicality of exponential annealing for convex optimization. In particular, inspired by interior-point methods, we propose modifying the hit-and-run random walk to bias iterates away from the boundary of the feasible region and show that this approach yields a substantial reduction in computational cost. We perform computational experiments for linear and semidefinite optimization problems. For linear optimization problems, we verify the correlation of phase count with the Renegar condition measure (described in [13]); for semidefinite optimization, we verify the correlation of phase count with a geometry measure (presented in [4]). en_US
dc.description.statementofresponsibility by Jeremy Chen. en_US
dc.format.extent 106 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 Computational issues and related mathematics of an exponential annealing homotropy for conic optimization 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 225095688 en_US


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