Transmission System Operator

\[\begin{aligned} \max_{\substack{q^{A}_{acmy}, \\ \Delta^{A}_{acy}, \\ \Delta^{RA}_{arcy}}} \quad & \sum_{y \in \mathcal{Y}} r_{y} \sum_{a \in \mathcal{A}} \left[ \begin{aligned} \sum_{c \in \mathcal{C} | (a,c) \in \mathcal{AC} } \left( \begin{aligned}\sum_{m \in \mathcal{M}} d_{m} \left( \pi^{A}_{acmy} - c^{A}_{acy} \right) q^{A}_{acmy} - \frac{1}{ \| \Delta \|_{y}} \frac{1}{2} c^{\Delta A}_{acy} \Delta^{A}_{acy} \end{aligned} \right) \\ - \frac{1}{ \| \Delta \|_{y}} \sum_{(r,c) \in \mathcal{RA} | (a,r) \in \mathcal{AC} } \frac{1}{2} c^{\Delta^{RA}}_{arcy} \Delta^{RA}_{arcy} \end{aligned} \right] \\ \text{s.t.} \quad % & q^{A}_{acmy} \leq \left( \begin{aligned} \Lambda^{A}_{acy} \\ + \sum_{ y' \in \mathcal{Y} | y-L^{A}_{c} \leq y'< y} \Delta^{A}_{acy}\\ + \sum_{r | (r,c) \in \mathcal{RA}} \sum_{ y' \in \mathcal{Y} | y-L^{A}_{c} \leq y'< y} f^{RA}_{rc} \Delta^{RA}_{arcy}\\ - \sum_{r | (c,r) \in \mathcal{RA}} \sum_{ y' \in \mathcal{Y} | y'< y} \Delta^{RA}_{acry} \end{aligned} \right) \quad & \begin{aligned} \forall (a,c) \in \mathcal{AC} , \\ m \in \mathcal{M}, y \in \mathcal{Y} \end{aligned} \quad & (\lambda^{A}_{acmy}) \\ % & \Delta^{A}_{acy} = \Delta^{A}_{a^{-1}(a)cy} \quad & \begin{aligned} \forall (a,c) \in \mathcal{AC} , \\ y \in \mathcal{Y} \end{aligned} \quad & (\delta^{A}_{acy}) \\ % & \Delta^{RA}_{arcy} = \Delta^{RA}_{a^{-1}(a)rcy} \quad & \begin{aligned} \forall a \in \mathcal{A}, (r,c) \in \mathcal{RA}, \\ (a,r) \in \mathcal{AC}, \\y \in \mathcal{Y} \end{aligned} \quad & (\delta^{RA}_{arcy}) \\ & q^{A}_{acmy}, \Delta^{A}_{acy}, \Delta^{RA}_{arcy} \geq 0 \quad & & \end{aligned}\]