Changes between Version 7 and Version 8 of OfficialTolArchiveNetworkBysPrior

Timestamp:

Dec 26, 2010, 12:00:52 AM (14 years ago)

Author:

Víctor de Buen Remiro

Comment:

--

OfficialTolArchiveNetworkBysPrior

@@ -76 +76 @@
 doesn't have any special behaviour for linear inequations, it could be an 
 inefficient implementation. However we can define just one non linear inequation 
-that is equivalent to the full set of linear inequations. If we define 
+that is equivalent to the full set of linear inequations. 
 
-[[LatexEquation( d\left(\beta\right)=A\beta-a=\left(d_{k}\left(\beta\right)\right)_{k=1\ldots r} )]]
-
-then
-
-[[LatexEquation( D_{k}\left(\beta\right)=\begin{cases} 0 & \forall d_{k}\left(\beta\right)\leq0\\ d_{k}\left(\beta\right) & \forall d_{k}\left(\beta\right)>0\end{cases} )]]
-
-is a continuous function in [[LatexEquation( \mathbb{R}^{n}  )]] and
-
-[[LatexEquation( D_{k}^{3}\left(\beta\right)=\begin{cases} 0 & \forall d_{k}\left(\beta\right)\leq0\\ d_{k}^{3}\left(\beta\right) & \forall d_{k}\left(\beta\right)>0\end{cases}  )]]
-
-is continuous and differentiable in [[LatexEquation( \mathbb{R}^{n} )]]
-
-[[LatexEquation( \frac{\partial D_{k}^{3}\left(\beta\right)}{\partial\beta_{i}}=\begin{cases} 0 & \forall d_{k}\left(\beta\right)\leq0\\ 3d_{k}^{2}\left(\beta\right)A_{ki} & \forall d_{k}\left(\beta\right)>0\end{cases}  )]]
-
-[[Image(source:/tolp/OfficialTolArchiveNetwork/BysPrior/doc/image004.png)]]
+||If we define [[BR]][[BR]] [[LatexEquation( d\left(\beta\right)=A\beta-a=\left(d_{k}\left(\beta\right)\right)_{k=1\ldots r} )]] then [[br]][[br]] [[LatexEquation( D_{k}\left(\beta\right)=\begin{cases} 0 & \forall d_{k}\left(\beta\right)\leq0\\ d_{k}\left(\beta\right) & \forall d_{k}\left(\beta\right)>0\end{cases} )]] [[br]][[br]] is a continuous function in [[LatexEquation( \mathbb{R}^{n}  )]] and [[br]][[br]] [[LatexEquation( D_{k}^{3}\left(\beta\right)=\begin{cases} 0 & \forall d_{k}\left(\beta\right)\leq0\\ d_{k}^{3}\left(\beta\right) & \forall d_{k}\left(\beta\right)>0\end{cases}  )]] [[br]][[br]] is continuous and differentiable in [[LatexEquation( \mathbb{R}^{n} )]] [[br]][[br]] [[LatexEquation( \frac{\partial D_{k}^{3}\left(\beta\right)}{\partial\beta_{i}}=\begin{cases} 0 & \forall d_{k}\left(\beta\right)\leq0\\ 3d_{k}^{2}\left(\beta\right)A_{ki} & \forall d_{k}\left(\beta\right)>0\end{cases}  )]] || [[Image(source:/tolp/OfficialTolArchiveNetwork/BysPrior/doc/image004.png)]] ||
 
 The feasibility condition can be defined as a single nonlinear