The OSCAR (octagonal selection and clustering algorithm for regression) regularizer consists of a `1 norm plus a pair-wise `∞ norm (responsible for its grouping behavior) and was proposed to encourage group sparsity in scenarios where the groups are a priori unknown. The OSCAR regularizer has a nontrivial proximity operator, which limits its applicability. We reformulate this regularizer as a w...

In the category of operator spaces, that is, subspaces of the bounded linear operators B(H) on a complex Hilbert space H together with the induced matricial operator norm structure, objects are equivalent if they are completely isometric, i.e. if there is a linear isomorphism between the spaces which preserves this matricial norm structure. Since operator algebras, that is, subalgebras of B(H),...