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.
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