Changes between Version 7 and Version 8 of OfficialTolArchiveNetworkBysPrior


Ignore:
Timestamp:
Dec 26, 2010, 12:00:52 AM (16 years ago)
Author:
Víctor de Buen Remiro
Comment:

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  • OfficialTolArchiveNetworkBysPrior

    v7 v8  
    7676doesn't have any special behaviour for linear inequations, it could be an
    7777inefficient implementation. However we can define just one non linear inequation
    78 that is equivalent to the full set of linear inequations. If we define
     78that is equivalent to the full set of linear inequations.
    7979
    80 [[LatexEquation( d\left(\beta\right)=A\beta-a=\left(d_{k}\left(\beta\right)\right)_{k=1\ldots r} )]]
    81 
    82 then
    83 
    84 [[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} )]]
    85 
    86 is a continuous function in [[LatexEquation( \mathbb{R}^{n}  )]] and
    87 
    88 [[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}  )]]
    89 
    90 is continuous and differentiable in [[LatexEquation( \mathbb{R}^{n} )]]
    91 
    92 [[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}  )]]
    93 
    94 [[Image(source:/tolp/OfficialTolArchiveNetwork/BysPrior/doc/image004.png)]]
     80||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)]] ||
    9581
    9682The feasibility condition can be defined as a single nonlinear