deletions | additions       diff --git a/The_Lagrangian_is_begin_multline__.tex b/The_Lagrangian_is_begin_multline__.tex  index 30a2ebf..8b568db 100644  --- a/The_Lagrangian_is_begin_multline__.tex  +++ b/The_Lagrangian_is_begin_multline__.tex 
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The Lagrangian is  \begin{multline}  L(\phi; \psi) = \sum_u \hat{c}_u g_u + -  \sum_{j\in N} \lambda_j\left(\sum_{i: ij\in L}p_{ij} + \sum_{u\in j} g_u - \sum_{u \in j} d_u \right) \\ + \sum_{(i,j)\in L} \left[\chi_{ij}( p_{ij} - B_{ij}(\theta_j - \theta_i)) + \sigma_{ij}(p_{ij} - p^{max}_{ij}) \right] + \\  + \sum_{i\in U} \left[\nu_u(g_u \left[\omega_u(g_u  - \hat{g}_u) - \omega_u \nu_u  g_u \right] \end{multline}