well in line with the phenomena in Fig \[fig:fig1\]. For the $L_1$-constrained case, the screening starts relatively at later stage than simplex case due to the fact that in Equation , two out of three terms are absolute values of some quantity and hence it is very tough to compensate both of them by the third quantity, in order for the entire sum to become negative. Hence in the beginning this rule can often be ineffective. As algorithm progresses, the duality gap becomes smaller and screening starts but at the same time the gradient (and therefore gap) also starts to decay which brings the trade-off shown in the plot. For both variants, screening becomes slow towards the end.

We also report the time taken to reach a duality gap of $10^{-7}$ with both the approaches mentioned above (simplex constrained and $L_1$-constrained) on for different datasets. The first two datasets (*Synth1* and *Synth2*) are generated under the same setting described earlier but *Synth1* with 5000 samples and *Synth2* with 10000 samples. *RCV1* is a real world dataset having $20,242$ samples and $47,236$ data dimensions. *news20Binary* is also a real world dataset having $19,996$ entries and $ 1,355,191$ dimensions. Below in Tables 