 $$\begin{aligned} \label{eqn:ineq_0_feasible_set} {{\left\vert\kern-0.00ex\left\vert\kern-0.00ex\left\vert (I-Z^{*}) Z (I-Z^{*})      \right\vert\kern-0.00ex\right\vert\kern-0.00ex\right\vert}}_{\ast} = &\, \sum_{k=0}^K \sum_{m\neq k} \frac{0}{n_k}\, \|Z_{G_{k}^{*} G_{m}^{*}}\|_{0} 