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abstract: 'We propose a new framework for deriving screening rules for convex optimization problems. Our approach covers a large class of constrained and penalized optimization formulations, and works in two steps. First, given any approximate point, the structure of the objective function and the duality gap is used to gather information on the optimal solution. In the second step, this information is used to produce screening rules, i.e. safely identifying unimportant weight variables of the optimal solution. Our general framework leads to a large variety of useful existing as well as new screening rules for many applications. For example, we provide new screening rules for general simplex and $L_1$-constrained problems, Elastic Net, squared-loss Support Vector Machines, minimum enclosing ball, as well as structured norm regularized problems, such as group lasso.'
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Introduction
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\[sec:intro\] [^1]Optimization techniques for high-dimensional problems have become the work-horses for most data-analysis and machine-learning methods. With the rapid increase of available data, major challenges occur as the number of optimization variables (weights) grows beyond capacity of current systems.

The idea of screening refers to eliminating optimization variables that are guaranteed to *not* contribute to any optimal solution, and can therefore safely be removed from problem. 