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|Title:||Algorithms for Large Scale Nuclear Norm Minimization and Convex Quadratic Semidefinite Programming Problems||Authors:||JIANG KAIFENG||Keywords:||Nuclear norm minimization, convex quadratic semidefinite programming, partial proximal point algorithm, inexact smoothing Newton method, inexact APG||Issue Date:||12-Aug-2011||Citation:||JIANG KAIFENG (2011-08-12). Algorithms for Large Scale Nuclear Norm Minimization and Convex Quadratic Semidefinite Programming Problems. ScholarBank@NUS Repository.||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.||URI:||http://scholarbank.nus.edu.sg/handle/10635/30701|
|Appears in Collections:||Ph.D Theses (Open)|
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