Algorithm 1 Enlarge_Cone$[\{{\mathbf{b}}_1,\dots ,{\mathbf{b}}_n\},\epsilon ]\to \{{\mathbf{\psi }}_1,\dots ,{\mathbf{\psi }}_n\}$.

Input: Set of nonnegative functions $\{{\mathbf{b}}_1,\dots ,{\mathbf{b}}_n\}$. Tolerance $\epsilon >0$.   for $i\in \{1,\dots ,n\}$ do     Set ${\sigma }_j^i=0,\forall j\ne i.$     for $\ell \in \{1,\dots ,n\}$ do       ${\alpha }_{\ell }^{i,*}=arg\; max\{\alpha \ge 0:\left[{\mathbf{b}}_i-{\sum }_{j\ne i}{\sigma }_j^i{\mathbf{b}}_j-\alpha {\mathbf{b}}_{\ell }\right]\left(t\right)>0,\forall t\in [0,T+\tau ]\}$       ${\sigma }_{\ell }^i={\sigma }_{\ell }^i+\frac{{\alpha }_{\ell }^{i,*}}{2}$        while ${\alpha }_{\ell }^{i,*}\ge \epsilon$ do         ${\alpha }_{\ell }^{i,*}=arg\; max\{\alpha \ge 0:\left[{\mathbf{b}}_i-{\sum }_{j\ne i}{\sigma }_j^i{\mathbf{b}}_j-\alpha {\mathbf{b}}_{\ell }\right]\left(t\right)>0,\forall t\in [0,T+\tau ]\}$         ${\sigma }_{\ell }^i={\sigma }_{\ell }^i+\frac{{\alpha }_{\ell }^{i,*}}{2}$        end while      end for     ${\mathbf{\psi }}_i={\mathbf{b}}_i-{\sum }_{j\ne i}{\sigma }_j^i{\mathbf{b}}_j$   end for Output:$\{{\mathbf{\psi }}_1,\dots ,{\mathbf{\psi }}_n\}$