deletions | additions       diff --git a/For_the_sake_of_briefness__.tex b/For_the_sake_of_briefness__.tex  index ff3417d..1ffd886 100644  --- a/For_the_sake_of_briefness__.tex  +++ b/For_the_sake_of_briefness__.tex 
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\nabla_{d_k}L &= -\bar{c} + \lambda_j - \nu^l_k + \nu^u_k = 0 \\  \nabla_{\theta_j}L &= -\sum_{i}\mu_{ij}B_{ij} + \sum_{k}\mu_{jk}B_{jk} = 0 \\  \nabla_{p_{ij}}L &= -\lambda_j + \mu_{ij} -\sigma_{ij}^l + \sigma_{ij}^u = 0 \\  \nabla_{b_{ij}}L %\nabla_{b_{ij}}L  &= -\mu_{ij}M + \sigma^l_{ij}p^{l}_{ij} - \sigma_{ij}^u p^{u}_{ij} + 2M\rho_{ij}^u= 0 \\ \nabla_{r_{ij}}L &= -\mu_{ij} - \rho^l_{ij} + \rho^u_{ij} = 0  \end{align}  The complementarity conditions