+\label{eq:obj2}
+\end{equation}
+where $\delta$ is a regularisation factor.
+This indeed introduces quadratic functions on variables $x_{hl}$ and
+$R_{h}$ and makes some of the functions strictly convex.
+
+The authors then apply a classical dual based approach with Lagrange multiplier
+to solve such a problem~\cite{PM06}.
+They first introduce dual variables
+$u_{hi}$, $v_{h}$, $\lambda_{i}$, and $w_l$ for any
+$h \in V$, $ i \in N$, and $l \in L$.
+
+\begin{equation}
+\begin{array}{l}
+L(R,x,P_{s},q,u,v,\lambda,w)=\\
+\sum_{i \in N} \left( q_i^2 + q_i. \left(
+\sum_{l \in L } a_{il}w_l-
+\lambda_iB_i
+\right)\right) \\
++ \sum_{h \in V} \left(
+v_h.\dfrac{\ln(\sigma^2/D_h)}{\gamma P_{sh} ^{2/3}} + \lambda_h P_{sh} \right)\\
++ \sum_{h \in V} \sum_{l\in L}
+\left(
+\delta.x_{hl}^2 \right.\\
+\qquad \qquad + x_{hl}.
+\sum_{i \in N} \left(
+\lambda_{i}.(c^s_l.a_{il}^{+} +
+c^r. a_{il}^{-} ) \right.\\
+\qquad \qquad\qquad \qquad +
+\left.\left. u_{hi} a_{il}
+\right)
+\right)\\
+ + \sum_{h \in V} \left(
+\delta R_{h}^2
+-v_h.R_{h} - \sum_{i \in N} u_{hi}\eta_{hi}\right)
+\end{array}
+\label{eq:dualFunction}
+\end{equation}