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We discuss how to evaluate the proximal operator of a convex and increasing function of a nuclear norm, which forms the key computational step in several first-order optimization algorithms such as (accelerated) proximal gradient descent and ADMM. Various special cases of the problem arise in low-rank matrix completion, dropout training in deep learning and high-order low-rank tensor recovery, although they have all been solved on a case-by-case basis. We provide an unified and efficiently computable procedure for solving this problem.
The problem of recovering a low-rank matrix from the linear constraints, known as affine matrix rank minimization problem, has been attracting extensive attention in recent years. In general, affine matrix rank minimization problem is a NP-hard. In o
We derive a formula for optimal hard thresholding of the singular value decomposition in the presence of correlated additive noise; although it nominally involves unobservables, we show how to apply it even where the noise covariance structure is not
Affine rank minimization problem is the generalized version of low rank matrix completion problem where linear combinations of the entries of a low rank matrix are observed and the matrix is estimated from these measurements. We propose a trainable d
This correspondence disproves the main results in the paper Design of Asymmetric Shift Operators for Efficient Decentralized Subspace Projection by S. Mollaebrahim and B. Beferull-Lozano. Counterexamples and counterproofs are provided when applicable
In this paper, we have developed a parallel branch and bound algorithm which computes the maximal structured singular value $mu$ without tightly bounding $mu$ for each frequency and thus significantly reduce the computational complexity.