R Under development (unstable) (2012-07-27 r60013) -- "Unsuffered Consequences"
Copyright (C) 2012 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i686-pc-linux-gnu (32-bit)

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> library(bbmle)
> x <- 0:10
> y <- c(26, 17, 13, 12, 20, 5, 9, 8, 5, 4, 8)
> d <- data.frame(x,y)
> fits <- lapply(c("optim","nlm","nlminb"),
+        mle2,
+        minuslogl=y~dpois(lambda=ymax/(1+x/xhalf)),
+        start=list(ymax=15,xhalf=6),data=d,
+        method="Nelder-Mead") ## 'method' is ignored by nlm()/nlminb()
Warning messages:
1: In dpois(x = c(26, 17, 13, 12, 20, 5, 9, 8, 5, 4, 8), lambda = c(31.4659916032255,  :
  NaNs produced
2: In nlm(f = objectivefunction, p = start, hessian = FALSE, ...) :
  NA/Inf replaced by maximum positive value
> sapply(fits,coef)
           [,1]      [,2]      [,3]
ymax  24.999725 24.999387 24.999424
xhalf  3.055245  3.055784  3.055781
> sapply(fits,logLik)
[1] -28.60406 -28.60405 -28.60405
> 
> (fit2 <-  mle2(y~dpois(lambda=25/(1+x/xhalf)),
+               start=list(xhalf=5),data=d,
+               lower=2,upper=8,
+               optimizer="optimize"))

Call:
mle2(minuslogl = y ~ dpois(lambda = 25/(1 + x/xhalf)), start = list(xhalf = 5), 
    optimizer = "optimize", data = d, lower = 2, upper = 8)

Coefficients:
   xhalf 
3.055659 

Log-likelihood: -28.6 
> 
> ## gives error referring to 'interval' rather than 'upper'/'lower'
> ## (fit2 <-  mle2(y~dpois(lambda=25/(1+x/xhalf)),
> ##              start=list(xhalf=5),
> ##              optimizer="optimize"))
> 
> proc.time()
   user  system elapsed 
  0.788   1.016   1.661