Screening Rules for Convex Problems

This thesis gives a general approach to deriving screening rules for convex optimization problems. It splits up in three steps. As the first step, the Karush-Kuhn-Tucker conditions are used to derive necessary conditions that allow to reduce the problem size. They depend on the optimal solution itself. The second step is to gather information on the optimal solution from a known approximation. In the third and final step the information is used to get conditions that do not depend on the optimal solution, which are then called screening rules. This thesis studies in particular the unit simplex, the unit box and polytopes as domain. The resulting screening rules can be applied to various problems, such as Support Vector Machines (SVM), the Minimum Enclosing Ball (MEB), LASSO problems and logistic regression. The resulting screening rules are compared to existing rules for those problems.