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dc.contributor.advisorDimitris J. Bertsimas.en_US
dc.contributor.authorSim, Melvynen_US
dc.contributor.otherMassachusetts Institute of Technology. Operations Research Center.en_US
dc.date.accessioned2005-06-02T18:24:20Z
dc.date.available2005-06-02T18:24:20Z
dc.date.copyright2004en_US
dc.date.issued2004en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/17725
dc.descriptionThesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2004.en_US
dc.descriptionIncludes bibliographical references (p. 169-171).en_US
dc.description.abstractWe propose new methodologies in robust optimization that promise greater tractability, both theoretically and practically than the classical robust framework. We cover a broad range of mathematical optimization problems, including linear optimization (LP), quadratic constrained quadratic optimization (QCQP), general conic optimization including second order cone programming (SOCP) and semidefinite optimization (SDP), mixed integer optimization (MIP), network flows and 0 - 1 discrete optimization. Our approach allows the modeler to vary the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations, while keeping the problem tractable. Specifically, for LP, MIP, SOCP, SDP, our approaches retain the same complexity class as the original model. The robust QCQP becomes a SOCP, which is computationally as attractive as the nominal problem. In network flows, we propose an algorithm for solving the robust minimum cost flow problem in polynomial number of nominal minimum cost flow problems in a modified network. For 0 - 1 discrete optimization problem with cost uncertainty, the robust counterpart of a polynomially solvable 0 - 1 discrete optimization problem remains polynomially solvable and the robust counterpart of an NP-hard o-approximable 0-1 discrete optimization problem, remains a-approximable.en_US
dc.description.abstract(cont.) Under an ellipsoidal uncertainty set, we show that the robust problem retains the complexity of the nominal problem when the data is uncorrelated and identically distributed. For uncorrelated, but not identically distributed data, we propose an approximation method that solves the robust problem within arbitrary accuracy. We also propose a Frank-Wolfe type algorithm for this case, which we prove converges to a locally optimal solution, and in computational experiments is remarkably effective.en_US
dc.description.statementofresponsibilityby Melvyn Sim.en_US
dc.format.extent171 p.en_US
dc.format.extent4979081 bytes
dc.format.extent4978895 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/pdf
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsM.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.urihttp://dspace.mit.edu/handle/1721.1/7582
dc.subjectOperations Research Center.en_US
dc.titleRobust optimizationen_US
dc.typeThesisen_US
dc.description.degreePh.D.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Operations Research Center
dc.contributor.departmentSloan School of Management
dc.identifier.oclc56462083en_US


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