Algorithm 2 OPT-Sent

$$\begin{array}{ll}\underset{\mathbf{w},{\xi }_i}{\text{minimize}}& {\Vert \mathbf{w}\Vert }_1+{\displaystyle \sum _{i=1}^{N^{\text{train}}}{\xi }_i^2}\\ \text{subject to}& {\displaystyle \sum _{k=1}^{N_i}{\displaystyle \sum _{j=1}^D{\mathbf{X}}_i}(k,j)\mathbf{w}(j)-s_i\le {\xi }_i}\\ & s_i-{\displaystyle \sum _{k=1}^{N_i}{\displaystyle \sum _{j=1}^D{\mathbf{X}}_i}(k,j)\mathbf{w}(j)\le {\xi }_i}\\ & \mathbf{w}\ge 0\end{array}$$