Barrier smoothing for nonsmooth convex minimization

This paper proposes a smoothing technique for nonsmooth convex minimization using self-concordant barriers. To illustrate the main ideas, we compare our technique and the proximity smoothing approach [1] via the classical gradient method on both the theoretical and numerical aspects. While the barrier smoothing approach maintains the sublinear-convergence rate, it affords a new analytic step size, which significantly enhances the practical convergence of the gradient method as compared to proximity smoothing.