Nolan,
You are correct that there is inconsistency. The feasible region should be ui
%*% theta - ci > 0, so that log(ui %*% theta - ci) is defined.
There is a more serious problem in termination criterion for iterations:
if (is.finite(r) && is.finite(r.old) && abs(r - r.old)/(outer.eps +
abs(r - r.old)) < outer.eps)
break
Ideally convergence is achieved when |r - r.old| is small. But according to
the above code, the logical condition inside the if(.) will be TRUE only when
abs(r - r.old) < (outer.eps)^2 (for small outer.eps). For example, let |r -
r.old| = outer.eps. The above condition becomes: if (0.5 < outer.eps) break,
which will obviously never happen for values of outer.eps < 1/2. Now, if
outer.eps = 1.e-05 (default) and we let |r - r.old| <= 1.e-10, then the above
condition will be satisfied.
In short, the termination criterion used is too stringent. Better termination
criteria are:
if (is.finite(r) && is.finite(r.old) && abs(r - r.old) < outer.eps)
break
or
if (is.finite(r) && is.finite(r.old) && abs(r - r.old)/(1 + abs(r +
r.old)/2) < outer.eps) break
Best,
Ravi.
-----Original Message-----
From: r-devel-boun...@r-project.org [mailto:r-devel-boun...@r-project.org] On
Behalf Of Duncan Murdoch
Sent: Thursday, June 17, 2010 4:38 AM
To: John Nolan
Cc: r-devel@r-project.org
Subject: Re: [Rd] constrOptim( ): conflict between help page and code
John Nolan wrote:
> There is a contradiction between what the help page says and what constrOptim
> actually
> does with the constraints. The issue is what happens on the boundary.
>
I don't know if this was a recent change, but the current help says:
"The starting value must be in the interior of the feasible region, but
the minimum may be on the boundary."
The boundary is not in the interior.
Duncan Murdoch
> The help page says
> The feasible region is defined by ‘ui %*% theta - ci >= 0’,
> but the R code for constrOptim reads
> if (any(ui %*% theta - ci <= 0))
> stop("initial value not feasible")
> The following example shows that when the initial point is on the boundary of
> the
> feasibility region, you get the above error message and execution stops.
>
>
>> fn <- function(x) { return(sum(x)) }
>>
>> ui <- diag(rep(1,2))
>> ci <- matrix(0,nrow=2,ncol=1)
>> constrOptim( c(0,0), fn, NULL, ui, ci )
>>
> Error in optim(theta.old, fun, gradient, control = control, method = method,
> :
> function cannot be evaluated at initial parameters
>
>> version
>>
> platform i386-pc-mingw32
> arch i386
> os mingw32
> system i386, mingw32
> status
> major 2
> minor 10.0
> year 2009
> month 10
> day 26
> svn rev 50208
> language R
> version.string R version 2.10.0 (2009-10-26)
>
> In contrast, at a different place in constrOptim - the internal function R -
> the boundary of the feasibility region is allowed: if (any(gi < 0))
> return(NaN),
> and it seems to explicitly allow boundaries at another place:
> allowing gi==0 and interpreting log(gi) as -Inf.
>
>
> John
>
> ...........................................................................
>
> John P. Nolan
> Math/Stat Department
> 227 Gray Hall
> American University
> 4400 Massachusetts Avenue, NW
> Washington, DC 20016-8050
>
> jpno...@american.edu
> 202.885.3140 voice
> 202.885.3155 fax
> http://academic2.american.edu/~jpnolan
> ...........................................................................
> ______________________________________________
> R-devel@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel
>
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