Dear Professor Lumley.
You are absolutely right! Please allow me to rephrase:
Assuming Professor Murdoch's explanation that theta=c(0.5,0.3,0.5) violate
the constrain while theta1=c(0.5,0.9,0.5) satisfies it.
I did the following
#########################
> theta=c(0.5,0.3,0.5)
> theta1=c(0.5,0.9,0.5)
> ui%*%theta-ci
[,1]
[1,] 0.5
[2,] 0.0
[3,] 0.3
[4,] 1.7
[5,] 0.5
[6,] 0.1
> ui%*%theta1-ci
[,1]
[1,] 0.5
[2,] 0.0
[3,] 0.9
[4,] 1.1
[5,] 0.5
[6,] 0.1
In both cases, all the elements in the resulting array are non-negative.
Which means, theta and thera1 either both satisfy or both violate the
constrain.
Best Wishes
Yuchen
On 9/11/07, Thomas Lumley <[EMAIL PROTECTED]> wrote:
>
> On Mon, 10 Sep 2007, Yuchen Luo wrote:
>
> > Dear Professor Murdoch.
> > Thank you for your help!
> > 1. I believe c(0.5,0.3,0.5) satisfies the constrain because I did the
> > following experiment
> > ui=-1*ui
> > ci=-1*ci
> > constrOptim(c(0.5,0.3,0.5), f=fit.error, gr=fit.error.grr, ui=ui,ci=ci)
> >
> > The same error message pops up. Any theta ( in this case, c(0.5,0.3,0.5
> ))
> > cannot violate both ui%*%theta>=ci and -ui%*%theta>=-ci.
>
> Why not? ui%*%theta>=ci is a six-dimensional constraint in your example,
> so a different element of the constraint can be violated.
>
> -thomas
>
>
>
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