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remove unnecessary constraints

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Yu Cong 2025-04-10 21:18:13 +08:00
parent 42a889e6ed
commit b4b4ff7291
2 changed files with 6 additions and 2 deletions
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@ -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*}