deletions | additions       diff --git a/The_complementarity_slackness_conditions_introduce__.tex b/The_complementarity_slackness_conditions_introduce__.tex  index 9969770..d1247b3 100644  --- a/The_complementarity_slackness_conditions_introduce__.tex  +++ b/The_complementarity_slackness_conditions_introduce__.tex 
...
\sum_{ij\in L^1}\left[ \mu_{ij}M(b_{ij}-1) + \rho^u_{ij}2M(1 - b_{ij}) + p^u_{ij} \sigma^u_{ij} b_{ij} - p^{l}_{ij} \sigma^l_{ij} b_{ij} \right ]  \end{multline}  There are four terms that are non-linear: one is the $\omega \hat{g}$, and three terms with $b_{ij}$.  All of them could be linearized using the techniques described in the first part.  Let us denote by $\dot{x}$ the special variable that replaces $x$ in equations and is bounded by  \begin{align*}  x&\leq \dot{x} + M(1-b)\leq M \\  0&\leq \dot{x}\leq x  \end{align*}  By adding the following conditions  \begin{align}