PRISMA: PRoximal Iterative SMoothing Algorithm

Abstract

Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and sparse inverse covariance selection, 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. We use a time variant smoothing strategy that allows us to obtain a guarantee that does not depend on knowing in advance the total number of iterations nor a bound on the domain.

References in corpus (2)

• High-Dimensional Graphical Model Selection Using ${\ell }_1$-Regularized Logistic Regression
• Convex Optimization without Projection Steps

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• Fast Nonsmooth Regularized Risk Minimization with Continuation
• Online Optimization for Large-Scale Max-Norm Regularization