The atomic norm formulation of OSCAR regularization with application to the Frank-Wolfe algorithm

This paper proposes atomic norm formulation of octagonal shrinkage and clustering algorithm for regression (OSCAR) regularization. The OSCAR regularizer can be reformulated using a decreasing weighted sorted ℓ
1
(DWSL1) norm (which is shown to be convex). We also show how, by exploiting an atomic norm formulation, the Ivanov regularization scheme involving the OSCAR regularizer can be handled using the Frank-Wolfe (also known as conditional gradient) method.