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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.
Appears in Collections:Ph.D Theses (Open)

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