Accelerated Gradient Descent Method for Projections onto the $\ell_{1}$ -Ball

We present a computationally efficient algorithm to solve the projection onto the ℓ
₁
-ball problem, which is cast as an equivalent univariate optimization problem by means of its dual formulation, the ℓ
_∞
proximity operator. Our algorithm, which is a customization of the Nesterov's accelerated gradient descent method, is empirically demonstrated to be faster than the state-of-the-art methods for the projection onto the ℓ
₁
-ball problem.