deletions | additions       diff --git a/section_Alternative_Formulation_We_reformulate__.tex b/section_Alternative_Formulation_We_reformulate__.tex  index c12682e..2d8404a 100644  --- a/section_Alternative_Formulation_We_reformulate__.tex  +++ b/section_Alternative_Formulation_We_reformulate__.tex 
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\begin{align*}  \sum_u \hat{c}_u g_u &\rightarrow min && \\  \sum_{i: ij\in L}p_{ij} &= \sum_{u\in j} g_u - \sum_{u \in j} d_u &&\forall j\in N &| &\lambda\\  p_{ij} &+ p_{ji} = k(p_{ij} - p_{ji})^2 \\  p_{ij} &= B_{ij}(\theta_j - \theta_i)&&\forall (i,j) && \\  p_{ij} &\leq p^{+}_{ij},&& \forall (i,j) \in L &| &\sigma_{ij} \\  0&\leq g_u \leq \hat{g}_u &&\forall u & | & v_u, g_u