the contribution of our paper is on the theoretical generality and the collection of new screening applications, we will still briefly illustrate the performance of some of the proposed screening algorithms, for the classical examples of simplex constrained and $L_1$-constrained problems. We compare the fraction of active variables and the Wolfe-Gap function as optimization algorithm progress. We consider the optimization problem of the form $\underset{{\bm{x}}\in {\mathcal{B}}_{L_1}}\min \|A{\bm{x}}- {\bm{b}}\|_2^2$. ${\mathcal{B}}_{L_1}$ is a scaled $L_1$-ball with radius $35$. $A \in \mathbb{R}^{3000\times600}$ is a random Gaussian matrix and a noisy measurement ${\bm{b}}= A{\bm{x}}^\star$ where ${\bm{x}}^\star$ is a sparse vector of $+1$ and $-1$ with only $70$ non zeros entries. We solve the above optimization problem using the Frank-Wolfe algorithm (pair-wise variant, see [@LacosteJulien:2015wj]). Before putting this optimization problem into the solver we convert this problem into the barycentric representation which is $\underset{{\bm{x}}_{{\triangle}} \in {\triangle}}\min \|A_{{\triangle}}{\bm{x}}_{{\triangle}} - {\bm{b}}\|_2^2$. The relation between the transformed variable and original variable can be given by $A_{{\triangle}} = [A\,|-A]$ and ${\bm{x}}= [I_n\,| - I_n]{\bm{x}}_{{\triangle}}$. For more details see [@Jaggi:2014co].

  -------------------- ------------------ ---------------
      **Dataset/**      **No Screening**   **Screening**
   **No. of Samples**    **(Simplex)**     **(Simplex)**
     *Synth1* 5000          13.1 sec          11.7sec
     *Synth2* 10000         28.3 sec         23.1 sec
      *RCV1* 20242          18.6 min         13.5 min
    *news20B* 