\begin{align}
 & \min_{k=1,\dots,N}\left\Vert \mathcal{G}\left(x_{k}^{md},\nabla\Psi\left(x_{k}^{md}\right),\omega_{k}\right)\right\Vert ^{2}\nonumber \\
 & \hspace{1.2 in} \leq \left[\sum_{k=1}^{N}\Gamma_{k}^{-1}\omega_{k}\left(1-L_{\Psi}\omega_{k}\right)\right]^{-1}\left[\frac{\left\Vert x_{0}-x^{*}\right\Vert ^{2}}{\delta_{1}}+\frac{2L_{h}}{\Gamma_{N}}\left(\left\Vert x^{*}\right\Vert ^{2}+M^{2}\right)\right].\label{eq:complexity-bound}
\end{align}
