diff --git a/main.pdf b/main.pdf index 238256f..7f1b388 100644 Binary files a/main.pdf and b/main.pdf differ diff --git a/main.tex b/main.tex index 28b0d1f..a5c4546 100644 --- a/main.tex +++ b/main.tex @@ -152,9 +152,13 @@ s.t.& & \sum_{e\in T} x_e+y_e&\geq 1 & &\forall T\quad \text{($x$ fo \end{aligned} \end{equation*} -Note that now this is almost a positive covering LP. Let $L(\lambda)= \min \{ w(C\setminus F)-\lambda(b-c(F)) | \forall \text{cut $C$}\;\forall F\subset C \land c(F)\leq b\}$ Consider the Lagrangian dual, +Note that now this is almost a positive covering LP. Let $L(\lambda)= \min \{ w(C\setminus F)-\lambda(b-c(F)) | \forall \text{cut $C$}\;\forall F\subset C +% \land c(F)\leq b +\}$ Consider the Lagrangian dual, \begin{equation*} -\max_{\lambda\geq 0} L(\lambda)= \max_{\lambda\geq 0} \min \left\{ w(C\setminus F)-\lambda(b-c(F)), \forall \text{cut $C$}\;\forall F\subset C \land c(F)\leq b\right\} +\max_{\lambda\geq 0} L(\lambda)= \max_{\lambda\geq 0} \min \left\{ w(C\setminus F)-\lambda(b-c(F)), \forall \text{cut $C$}\;\forall F\subset C +% \land c(F)\leq b +\right\} \end{equation*}