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Title: | Structured Low Rank Matrix Optimization Problems: A Penalty Approach | Authors: | GAO YAN | Keywords: | structured low rank matrix, a proximal subgradient method, a penalty approach, a smoothing Newton-BiCGStab method | Issue Date: | 19-Aug-2010 | Citation: | GAO YAN (2010-08-19). Structured Low Rank Matrix Optimization Problems: A Penalty Approach. ScholarBank@NUS Repository. | Abstract: | In this thesis, we study a class of structured low rank matrix optimization problems (SLR-MOPs) which aim at finding an approximate matrix of certain specific structures and whose rank is no more than a prescribed number. This kind of approximation is needed in many important applications arising from a wide range of fields. The SLR-MOPs are in general non-convex and thus difficult to solve due to the presence of the rank constraint. In this thesis, we propose a penalty approach to deal with this difficulty. Some rationale to motivate this penalty technique is also addressed. We further present a general proximal subgradient method for the purpose of solving the penalized problem. Finally, we design a quadratically convergent smoothing Newton-BiCGStab method to solve the resulted sub-problems. Numerical results indicate that our approach is able to handle both the rank and the linear constraints effectively, in particular in the situations when the rank is not very small. | URI: | http://scholarbank.nus.edu.sg/handle/10635/23706 |
Appears in Collections: | Ph.D Theses (Open) |
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