PRISMA: PRoximal Iterative SMoothing Algorithm

Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and basis pursuit, we propose a novel optimization algorithm for minimizing a convex objective which decomposes into three parts: a smooth part, a simple non-smooth Lipschitz part, and a simple non-smooth non-Lipschitz part. Our algorithm combines the methodology of forward-backward splitting, smoothing, and accelerated proximal methods.