Such screening techniques have received increased interest in several machine learning related applications in recent years, and have been shown to lead to very significant computational efficiency improvements in various cases, in particular for many types of sparse methods. Screening techniques can be used either as a pre-processing before passing the problem to the optimizer, or also interactively during any iterative solver (called dynamic screening), to gradually reduce the problem complexity during optimization.

While existing screening methods were mainly relying on geometric and problem-specific properties, we in this paper take a different approach. We propose a new framework allowing screening on general convex optimization problems, using simple tools from convex duality instead of any geometric arguments. Our framework applies to a very large class of optimization problems both for constrained as well as penalized problems, including most machine learning methods of interest.

Our main contributions in this paper are summarized as follows:

1.  We propose a new framework for screening for a more general class of optimization problem with a simple primal-dual structure.

2.  The framework leads to a large set of new screening rules for machine learning problems that could not be screened before. Furthermore, it also recovers many 