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Nuclear norm optimization and its application to observation model specification. (English) Zbl 1352.65165

Carmi, Avishy Y. (ed.) et al., Compressed sensing and sparse filtering. Berlin: Springer (ISBN 978-3-642-38397-7/hbk; 978-3-642-38398-4/ebook). Signals and Communication Technology, 95-122 (2014).
Summary: Optimization problems involving the minimization of the rank of a matrix subject to certain constraints are pervasive in a broad range of disciples, such as control theory, signal processing, and machine learning. However, solving such rank minimization problems is usually very difficult as they are NP-hard in general. The nuclear norm of a matrix, as the tightest convex surrogate of the matrix rank, has fueled much of the recent research and has proved to be a powerful tool in many areas. In this chapter, we aim to provide a brief review of some of the state-of-the-art in nuclear norm optimization algorithms as they relate to applications. We then propose a novel application of the nuclear norm to the linear model recovery problem, as well as a viable algorithm for solution of the recovery problem. Preliminary numerical results presented here motivates further investigation of the proposed idea.
For the entire collection see [Zbl 1275.94004].

MSC:

65K10 Numerical optimization and variational techniques
65F99 Numerical linear algebra
15A24 Matrix equations and identities
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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