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https://scholarbank.nus.edu.sg/handle/10635/30701
DC Field | Value | |
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dc.title | Algorithms for Large Scale Nuclear Norm Minimization and Convex Quadratic Semidefinite Programming Problems | |
dc.contributor.author | JIANG KAIFENG | |
dc.date.accessioned | 2012-02-29T18:00:47Z | |
dc.date.available | 2012-02-29T18:00:47Z | |
dc.date.issued | 2011-08-12 | |
dc.identifier.citation | JIANG KAIFENG (2011-08-12). Algorithms for Large Scale Nuclear Norm Minimization and Convex Quadratic Semidefinite Programming Problems. ScholarBank@NUS Repository. | |
dc.identifier.uri | http://scholarbank.nus.edu.sg/handle/10635/30701 | |
dc.description.abstract | In this thesis, we focus on designing efficient algorithms for solving large scale nuclear norm minimization and convex quadratic semidefinite programming (QSDP) problems. We introduce a partial proximal point algorithm for solving nuclear norm regularized matrix least squares problems with equality and inequality constraints. The inner sub-problems, reformulated as a system of semismooth equations, are solved by an inexact smoothing Newton method, which is proved to be quadratically convergent under a constraint non-degeneracy condition, together with the strong semi-smoothness property of the singular value soft thresholding operator. To solve convex QSDP problems, we extend the accelerated proximal gradient method to the inexact setting where the sub-problems need only be solved with progressively better accuracy, and show that it enjoys the same superior worst-case iteration complexity as the exact counterpart. Numerical experiments on a variety of large scale nuclear norm minimization and convex QSDP problems show that the proposed algorithms are very efficient and robust. | |
dc.language.iso | en | |
dc.subject | Nuclear norm minimization, convex quadratic semidefinite programming, partial proximal point algorithm, inexact smoothing Newton method, inexact APG | |
dc.type | Thesis | |
dc.contributor.department | MATHEMATICS | |
dc.contributor.supervisor | TOH KIM CHUAN | |
dc.description.degree | Ph.D | |
dc.description.degreeconferred | DOCTOR OF PHILOSOPHY | |
dc.identifier.isiut | NOT_IN_WOS | |
Appears in Collections: | Ph.D Theses (Open) |
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