Efficient projection onto the infinity-1 ball using Newton's root-finding methodCP1

The projection onto the $\ell_{1,\infty}$ ball (P$\ell_{1,\infty}$) has been applied in cognitive neuroscience and classification tasks, and it is an example of mixed norms, which recently have gained popularity for inducing group sparsity priors in several applications. We present a new algorithm, eight times faster than the state-of-the-art, to solve P$\ell_{1,\infty}$ for which we have derived an analytical expression that allows us to apply Newton’s root-finding method along with an effective pruning strategy.

This presentation is part of Contributed Presentation “CP1 - Contributed session 1

Gustavo Chau (Pontificia Universidad Catolica del Peru)
Brendt Wohlberg (Los Alamos National Laboratory)
Paul Rodriguez (Pontificia Universidad Catolica del Peru)
inverse problems, mixed norms, nonlinear optimization, projection, root finding