survey paper by [@Xiang:2014vi] for an overview of geometric methods for Lasso screening. Sphere-region based methods differ from dome-shaped regions as used in [@Ghaoui:2010tu] in choosing different centers and radii to bound the dual optimal point. Apart from being geometry specific, most existing approaches such as [@Wang:2013uq; @Wang:2014un; @Liu:2014uz; @Ghaoui:2010tu; @Ogawa:2013ul] are not agnostic to the regularization parameter used, but instead are restricted to perform screening along the entire regularization path (as the regularization parameter changes). This is known as sequential screening, and restricts its usability to optimization algorithms obtaining paths. In contrast, our proposed framework here allows any internal optimization algorithms to be equipped with screening.

Despite the importance of constrained problems in many applications, much less is known about screening for constrained optimization, in contrast to the case of penalized optimization problems. For the dual of the hinge loss SVM, which is a box-constrained optimization problem, [@Ogawa:2014vw] proposed a geometric screening rule based on the intersection region of two spheres, in the sequential setting of varying regularizer. More recently, [@Zimmert:2015ue] provided new screening rules for that case in the dynamic setting using a method similar to our approach. However their method is restricted to the SVM case.

As 