a first step to allow screening for more general optimization objectives, [@Ndiaye:2015wj] gives duality gap based screening rules for multi-task and multi-class problems (in the penalized setting) under for a wider class of objectives $f$. Nevertheless, their approach is restricted to assume separability of $f$ over the group structure, which limits the screening rules, in the sense of not covering standard group lasso for example. Also in [@Shibagaki:2016ts], authors assume the similar problem formulation as in [@Ndiaye:2015wj] but a bit more general. The focus in [@Shibagaki:2016ts] is on screening rules for SVM problems rather than general framework. They derive the screening rules for SVM by considering standard hinge and $\epsilon$-insensitive loss with regularization formulation which is close to the empirical risk minimization framework here, but has more limited applications in terms of generalization of the screening rules. We here provide screening rules for a more general framework of box constrained optimization, while hinge-loss SVM happens to be a special case of this. Our proposed approach can be shown to recover many of the other existing rules including e.g. [@Ndiaye:2015wj] and [@Zimmert:2015ue], but significantly generalizing the method to general objectives and constraints as well as regularizers. The rest of the paper 