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Efficient Proximal Mapping Computation for Unitarily Invariant Low-Rank Inducing Norms. (arXiv:1810.07570v1 [math.OC])
来源于:arXiv
Low-rank inducing unitarily invariant norms have been introduced to convexify
problems with low-rank/sparsity constraint. They are the convex envelope of a
unitary invariant norm and the indicator function of an upper bounding rank
constraint. The most well-known member of this family is the so-called nuclear
norm. To solve optimization problems involving such norms with proximal
splitting methods, efficient ways of evaluating the proximal mapping of the
low-rank inducing norms are needed. This is known for the nuclear norm, but not
for most other members of the low-rank inducing family. This work supplies a
framework that reduces the proximal mapping evaluation into a nested binary
search, in which each iteration requires the solution of a much simpler
problem. This simpler problem can often be solved analytically as it is
demonstrated for the so-called low-rank inducing Frobenius and spectral norms.
Moreover, the framework allows to compute the proximal mapping of compositions
of the 查看全文>>