2018
DOI: 10.1109/tac.2018.2813009
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Low-Rank Optimization With Convex Constraints

Abstract: The problem of low-rank approximation with convex constraints, which appears in data analysis, system identification, model order reduction, low-order controller design and low-complexity modelling is considered. Given a matrix, the objective is to find a low-rank approximation that meets rank and convex constraints, while minimizing the distance to the matrix in the squared Frobenius norm. In many situations, this non-convex problem is convexified by nuclear norm regularization. However, we will see that the … Show more

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Cited by 42 publications
(59 citation statements)
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“…The following example is a case study for the proposed algorithm and the analysis on the tight relaxation. Consider the following rank-1 matrix (3), where Σ =Ω + ∆ > 0,Ω is given in (14), and ∆ is generated according to (16) for T = 100 times with each level of ∆ F .…”
Section: B Case Studymentioning
confidence: 99%
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“…The following example is a case study for the proposed algorithm and the analysis on the tight relaxation. Consider the following rank-1 matrix (3), where Σ =Ω + ∆ > 0,Ω is given in (14), and ∆ is generated according to (16) for T = 100 times with each level of ∆ F .…”
Section: B Case Studymentioning
confidence: 99%
“…A series of matrix norms, called the r * -norms (or spectral r-support norms) [16]- [18], are defined by M l∞,r * := max…”
Section: B Low-rank Inducing R * -Normmentioning
confidence: 99%
“…Since the submission of this article the two related papers [8] and [7] have appeared. In [8] the convex envelope of (1.6) and its proximal operator are computed.…”
Section: I(a) = R K (A)mentioning
confidence: 99%
“…In [8] the convex envelope of (1.6) and its proximal operator are computed. In [7] these results are generalized to arbitrary unitarily invariant norms when F = 0.…”
Section: I(a) = R K (A)mentioning
confidence: 99%
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