Efficient Proximal Mapping Computation for Low-Rank Inducing Norms

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 norm and indicator function an upper bounding rank The most well-known member this family is so-called nuclear norm. To solve optimization involving such proximal splitting methods, efficient ways evaluating mapping low-rank needed. This known for norm, but not other members family. work supplies framework that reduces evaluation into nested binary search, in which each iteration requires solution much simpler problem. problem can often be solved analytically as it demonstrated Frobenius spectral norms. Moreover, allows compute compositions these increasing functions projections onto their epigraphs. has additional advantage we also deal methods.