R help - May 2008 - Solution of function

Hi,
   
  I want to find solution of function :  f(x,y) = x'Cx - a under constraints
:
   
  0 < x,y < p
  0 < x-y< q
   
  where a, p,q are given constants and x = (x, y) and C is a 2X2 matrix (given)
   
  Can anyone suggest me any R function to do that?
   
   

       
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Megh Dal wrote:
> Hi,
>    
>   I want to find solution of function :  f(x,y) = x'Cx - a under
constraints :
>    
>   0 < x,y < p
>   0 < x-y< q
>    
>   where a, p,q are given constants and x = (x, y) and C is a 2X2 matrix
(given)
>    
>   Can anyone suggest me any R function to do that?
>    
>   
Not likely. What you have (if C is  positive definite) is the
intersection between the boundary of an ellipse and the interior of a
parallelepiped, where the center of the ellipse and one corner of the
parallelepiped is at (0,0).

This is the union of between zero and three curve segments (hmm, maybe
only two) and I don't think any of the standard solvers and minimizers
can come up with that kind of result.

-- 
   O__  ---- Peter Dalgaard             ?ster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907

Still I did not find any suggestion. Is my problem not elaborate enough?

Megh Dal <megh700004@yahoo.com> wrote:   I think I should be clear exactly
what I want :

take following example :

a = b = seq(1, 50000, by=500)
 v = matrix(0, nrow=length(a), ncol=length(a))
 for (i in 1:length(a))
   {
    for (j in 1:length(a))
       {
        d = c(17989*a[i], -18109*b[j])
        v[i,j] = t(d) %*% matrix(c(0.0001741, 0.0001280, 0.0001280,
0.0002570), nrow=2) %*% d
       }
   }
 library("rgl")
 open3d()
 persp3d(a,b,v,col="green",alpha=0.7,aspect=c(1,1,0.5))
shade <- outer(a, b, function(x,y) (0 < (x-y)) & ((x-y) < 20000))
 persp3d(a,b,v,col=ifelse(shade, "red", "green"),
alpha=0.7,aspect=c(1,1,0.5))


Here you see that the surface is the plot of a x'Cx for different values of
components of x. And the red region is the portion of that plot that satisfy 0
<x-y < 20000..

Now suppose user choose a point on red portion of that surface. Now I have to
tell (through some computationally efficient way) what is the corresponding
component values of x.

Any suggestion please?



 
Peter Dalgaard <P.Dalgaard@biostat.ku.dk> wrote:   Megh Dal
wrote:
> Hi,
> 
> I want to find solution of function : f(x,y) = x'Cx - a under
constraints :
> 
> 0 < x,y < p
> 0 < x-y< q
> 
> where a, p,q are given constants and x = (x, y) and C is a 2X2 matrix
(given)
> 
> Can anyone suggest me any R function to do that?
> 
> 
Not likely. What you have (if C is positive definite) is the
intersection between the boundary of an ellipse and the interior of a
parallelepiped, where the center of the ellipse and one corner of the
parallelepiped is at (0,0).

This is the union of between zero and three curve segments (hmm, maybe
only two) and I don't think any of the standard solvers and minimizers
can come up with that kind of result.

-- 
O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B
c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk) FAX: (+45) 35327907



    
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