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Regularization Paths for Re-Weighted Nuclear Norm Minimization
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DOI：10.1109/LSP.2015.2450505.png)
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We consider a class of weighted nuclear norm optimization problems with important applications in signal processing, system identification, and model order reduction. The nuclear norm is commonly used as a convex heuristic for matrix rank constraints. Our objective is to minimize a quadratic cost subject to a nuclear norm constraint on a linear function of the decision variables, where the trade-off between the fit and the constraint is governed by a regularization parameter. The main contribution is an algorithm to determine the so-called approximate regularization path, which is the optimal solution up to a given error tolerance as a function of the regularization parameter. The advantage is that we only have to solve the optimization problem for a fixed number of values of the regularization parameter, with guaranteed error tolerance. The algorithm is exemplified on a weighted Hankel matrix model order reduction problem.
Keyword:
Re-weighted hankel matrix nuclear norm minimization
regularization path
weighted H-2 model reduction
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9.6
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1.1W
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1.7W
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