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Semidefinite relaxation based branch-and-bound method for nonconvex quadratic programming

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dc.contributor.advisor Pablo A. Parrilo. en_US
dc.contributor.author Hu, Sha, 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 2007-10-19T20:32:26Z
dc.date.available 2007-10-19T20:32:26Z
dc.date.copyright 2006 en_US
dc.date.issued 2006 en_US
dc.identifier.uri http://hdl.handle.net/1721.1/39217
dc.description Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006. en_US
dc.description Includes bibliographical references (leaves 73-75). en_US
dc.description.abstract In this thesis, we use a semidefinite relaxation based branch-and-bound method to solve nonconvex quadratic programming problems. Firstly, we show an interval branch-and-bound method to calculate the bounds for the minimum of bounded polynomials. Then we demonstrate four SDP relaxation methods to solve nonconvex Box constrained Quadratic Programming (BoxQP) problems and the comparison of the four methods. For some lower dimensional problems, SDP relaxation methods can achieve tight bounds for the BoxQP problem; whereas for higher dimensional cases (more than 20 dimensions), the bounds achieved by the four Semidefinite programming (SDP) relaxation methods are always loose. To achieve tight bounds for higher dimensional BoxQP problems, we combine the branch-and-bound method and SDP relaxation method to develop an SDP relaxation based branch-and-bound (SDPBB) method. We introduce a sensitivity analysis method for the branching process of SDPBB. This sensitivity analysis method can improve the convergence speed significantly. en_US
dc.description.abstract (cont.) Compared to the interval branch-and-bound method and the global optimization software BARON, SDPBB can achieve better bounds and is also much more efficient. Additionally, we have developed a multisection algorithm for SDPBB and the multisection algorithm has been parallelized using Message Passing Interface (MPI). By parallelizing the program, we can significantly improve the speed of solving higher dimensional BoxQP problems. en_US
dc.description.statementofresponsibility by Sha Hu. en_US
dc.format.extent 75 leaves 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
dc.subject Computation for Design and Optimization Program. en_US
dc.title Semidefinite relaxation based branch-and-bound method for nonconvex quadratic programming 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 85844312 en_US


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