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The ordered weighted $\ell_1$ (OWL) norm is a newly developed generalizationof the Octogonal Shrinkage and Clustering Algorithm for Regression (OSCAR)norm. This norm has desirable statistical properties and can be used to performsimultaneous clustering and regression. In this paper, we show how to computethe projection of an $n$-dimensional vector onto the OWL norm ball in$O(n\log(n))$ operations. In addition, we illustrate the performance of ouralgorithm on a synthetic regression test.

An $O(n\log(n))$ Algorithm for Projecting Onto the Ordered Weighted $\ell_1$ Norm Ball