diff options
Diffstat (limited to 'graf/n6.lyx')
| -rw-r--r-- | graf/n6.lyx | 28 |
1 files changed, 14 insertions, 14 deletions
diff --git a/graf/n6.lyx b/graf/n6.lyx index e296d0b..6bf574a 100644 --- a/graf/n6.lyx +++ b/graf/n6.lyx @@ -222,11 +222,11 @@ teorema \end_inset , -\begin_inset Formula $P:=\{[x,y]\in\mathbb{R}^{p+q}:Ax+Gy\leq b\}$ +\begin_inset Formula $P:=\{[x,y]\in\mathbb{R}^{p+q}\mid Ax+Gy\leq b\}$ \end_inset y -\begin_inset Formula $S:=\{[x,y]\in P:x\in\mathbb{Z}^{p}\}$ +\begin_inset Formula $S:=\{[x,y]\in P\mid x\in\mathbb{Z}^{p}\}$ \end_inset , existen @@ -242,7 +242,7 @@ teorema \end_inset tales que -\begin_inset Formula $\text{ec}S=\{[x,y]:A'x+G'y\leq b'\}$ +\begin_inset Formula $\text{ec}S=\{[x,y]\mid A'x+G'y\leq b'\}$ \end_inset . @@ -253,11 +253,11 @@ teorema Demostración: \series default Sean -\begin_inset Formula $S:=\{(x,y)\in\mathbb{Z}^{2}:y\leq\sqrt{2}x,x\geq0,y\geq0\}$ +\begin_inset Formula $S:=\{(x,y)\in\mathbb{Z}^{2}\mid y\leq\sqrt{2}x,x\geq0,y\geq0\}$ \end_inset y -\begin_inset Formula $C:=\{(x,y):y<\sqrt{2}x,x\geq0,y\geq0\}\cup\{0\}$ +\begin_inset Formula $C:=\{(x,y)\mid y<\sqrt{2}x,x\geq0,y\geq0\}\cup\{0\}$ \end_inset . @@ -406,7 +406,7 @@ Sean \end_inset y -\begin_inset Formula $P:=\{x\in\mathbb{R}^{n}:Ax\leq b\}$ +\begin_inset Formula $P:=\{x\in\mathbb{R}^{n}\mid Ax\leq b\}$ \end_inset , si @@ -706,7 +706,7 @@ Lema de Veinott-Dantzig: \end_inset , -\begin_inset Formula $Q:=\{x\in\mathbb{R}^{n}:Ax=b,x\geq0\}$ +\begin_inset Formula $Q:=\{x\in\mathbb{R}^{n}\mid Ax=b,x\geq0\}$ \end_inset es entero. @@ -913,7 +913,7 @@ Teorema de Hoffman-Kruskal: \end_inset , el poliedro -\begin_inset Formula $\{x\in\mathbb{R}^{n}:Ax\leq b,x\geq0\}$ +\begin_inset Formula $\{x\in\mathbb{R}^{n}\mid Ax\leq b,x\geq0\}$ \end_inset es entero. @@ -978,7 +978,7 @@ Dada una submatriz \end_inset es unimodular, con lo que -\begin_inset Formula $Q:=\{[x,y]\in\mathbb{R}^{n+m}:Ax+Iy=b,[x,y]\geq0\}$ +\begin_inset Formula $Q:=\{[x,y]\in\mathbb{R}^{n+m}\mid Ax+Iy=b,[x,y]\geq0\}$ \end_inset es entero. @@ -1003,7 +1003,7 @@ Dada una submatriz \end_inset es -\begin_inset Formula $P:=\{x\in\mathbb{R}^{n}:b=b,x\geq0,b-Ax\geq0\}=\{Ax\leq b,x\geq0\}$ +\begin_inset Formula $P:=\{x\in\mathbb{R}^{n}\mid b=b,x\geq0,b-Ax\geq0\}=\{Ax\leq b,x\geq0\}$ \end_inset . @@ -1069,11 +1069,11 @@ Sean \end_inset , -\begin_inset Formula $P:=\{x:Ax\leq b,x\geq0\}$ +\begin_inset Formula $P:=\{x\mid Ax\leq b,x\geq0\}$ \end_inset , -\begin_inset Formula $Q:=\{[x,y]:Ax+y=b,[x,y]\geq0\}$ +\begin_inset Formula $Q:=\{[x,y]\mid Ax+y=b,[x,y]\geq0\}$ \end_inset y @@ -1643,7 +1643,7 @@ Otra posible formulación, con las mismas variables resulta de cambiar la \begin_layout Standard Para el problema del viajante de comercio sobre una red completa -\begin_inset Formula $R:=(V:=\{0,\dots,n-1\},E:=\{\{i,j\}\}_{i,j\in V,i\neq j},d)$ +\begin_inset Formula $R:=(V:=\{0,\dots,n-1\},E\mid =\{\{i,j\}\}_{i,j\in V,i\neq j},d)$ \end_inset , existen varias formulaciones: @@ -1783,7 +1783,7 @@ es & \min & {\textstyle \sum}_{ij}d_{ij}x_{ij}\\ & & {\textstyle \sum_{(i,j)\in E}}x_{ij} & =1 & & \forall i\\ & & {\textstyle \sum_{(k,i)\in E}}x_{ki} & =1 & & \forall i\\ - & & u_{i}-u_{j}+nx_{ij} & \leq n-1 & & \forall i,j\in\{1,\dots,n-1\}:(i,j)\in E\\ + & & u_{i}-u_{j}+nx_{ij} & \leq n-1 & & \forall i,j\in\{1,\dots,n-1\}\mid (i,j)\in E\\ & & x_{ij} & \in\{0,1\} & & \forall i,j\\ & & u_{i} & \in\mathbb{R}^{>0} & & \forall i \end{alignat*} |