deletions | additions       diff --git a/The_complementarity_slackness_conditions_introduce__.tex b/The_complementarity_slackness_conditions_introduce__.tex  index c1a2e7d..f87501b 100644  --- a/The_complementarity_slackness_conditions_introduce__.tex  +++ b/The_complementarity_slackness_conditions_introduce__.tex 
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0\leq\dot\sigma^{u,l}_{ij} &\leq \sigma^{u,l}_{ij}\\  \mu_{ij}\leq \dot{\mu}_{ij} + b_{ij}M &\leq M\\  \rho^u_{ij} \leq\dot\rho^u_{ij} + b_{ij}M&\leq M \\  \sigma^{u,l}_{ij} \leq\dot\sigma^{u,l}_{ij} + b_{ij}M&\leq (1 - b_{ij})M&\leq  M \end{align}  we get  \begin{multline} 
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\sum_{ij\in L^1}\left[ -\dot\mu_{ij}M + \dot\rho^u_{ij}2M + p^u_{ij} \dot\sigma^u_{ij} - p^{l}_{ij} \dot\sigma^l_{ij} \right ]  \end{multline}  The $\omega \hat{g}$ expression is linearized using the techniques described in section 1.  Let $\hat{g}_u = \sum a_i x_i^u + a_0$