A Projection Proximal-Point Algorithm for ℓ1 Minimization

Abstract

The problem of the minimization of least squares functionals with ℓ1 penalties is considered in an infinite dimensional Hilbert space setting. Though there are several algorithms available in the finite dimensional setting there are only a few of them that come with a proper convergence analysis in the infinite dimensional setting. In this work we provide an algorithm from a class that has not been considered for ℓ1 minimization before, namely, a proximal-point method in combination with a projection step. We show that this idea gives a simple and easy-to-implement algorithm. We present experiments that indicate that the algorithm may perform better than other algorithms if we employ them without any special tricks. Hence, we may conclude that the projection proximal-point idea is a promising idea in the context of ℓ1 minimization.