R help - Sep 2008 - To find vector X under contraints

Hi R,

 

I have the variance-covariance matrix,

 
>V=matrix(c(0.011119238, 0.002407527, 0.002407527, 0.020739401),2,2)
 

I need to find a vector X=c(x1,x2), such that 

1) X'VX is equal to a constant 2 (say) and 

2) sum(x) should be equal to a another constant 1.5 (say).

 

How do we do this in R?

 

 

BR, Shubha

Shubha Karanth | Amba Research

Ph +91 80 3980 8031 | Mob +91 94 4886 4510 

Bangalore * Colombo * London * New York * San José * Singapore *
www.ambaresearch.com

 

 

This e-mail may contain confidential and/or privileged i...{{dropped:13}}

Shubha Vishwanath Karanth wrote:
> Hi R,
> 
>  
> 
> I have the variance-covariance matrix,
> 
>  
> 
>> V=matrix(c(0.011119238, 0.002407527, 0.002407527, 0.020739401),2,2)
> 
>  
> 
> I need to find a vector X=c(x1,x2), such that 
> 
> 1) X'VX is equal to a constant 2 (say) and 
> 
> 2) sum(x) should be equal to a another constant 1.5 (say).
> 
>  
> 
> How do we do this in R?
You can try to optimize using optim() with an appropriate function to be 
minimized such as f(X) = (X'VX-2)^2 + (sum(X)-1.5)^2

Uwe Ligges




>  
> 
>  
> 
> BR, Shubha
> 
> Shubha Karanth | Amba Research
> 
> Ph +91 80 3980 8031 | Mob +91 94 4886 4510 
> 
> Bangalore * Colombo * London * New York * San Jos? * Singapore *
www.ambaresearch.com
> 
>  
> 
>  
> 
> This e-mail may contain confidential and/or privileged i...{{dropped:13}}
> 
> 
> 
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> 
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