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 <tlumley@u.washington.edu> 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
>
>
>

	[[alternative HTML version deleted]]

