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A penalty decomposition method for rank minimization problem with affine constraints. (English) Zbl 1443.93011

Summary: The rank minimization problem with affine constraints is widely applied in the fields of control, system identification, and machine learning, and attracted much attention and well studied in the past few years. Unlike most of the existing methods where a nuclear norm is used to approximate the rank term, in this paper, we apply the penalty decomposition method to solve the rank minimization problem directly. One subproblem can be solved effectively by using linear conjugate gradient method, and the other one has closed-form solutions by taking full use of the problem’s favorable structure. Under some suitable assumptions, the convergence results for the proposed method are given. Finally, we do numerical experiments on randomly generated and real data, the results show that the proposed method is effective and promising.

MSC:

93-10 Mathematical modeling or simulation for problems pertaining to systems and control theory
68T05 Learning and adaptive systems in artificial intelligence

Software:

ADMiRA
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Full Text: DOI

References:

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