R help - Apr 2008 - disturbing seed dependence in optim L-BFGS-B method

The the use of optim with the L-BFGS-B method for the following simple 
function gives erroneous results.  Any help appreciated!

Best,
Bob Reilly

# Code:

V=function(p){
p1=p[1];p2=p[2]
y=p1*p2-.4*(p1+p2)
return(-y)}

p=c(.2,.2) # p=c(.8,.8)

max=optim(p,V,method = "L-BFGS-B",lower=c(0,0),upper=c(1,1))
max1=optim(max$par,V,method = "L-BFGS-B",lower=c(0,0),upper=c(1,1))
max2=optim(max1$par,V,method = "L-BFGS-B",lower=c(0,0),upper=c(1,1))

max$par
max1$par
max2$par

-max2$value

-V(c(1,1)) # true maximum occurs at c(1,1)
# setting the seed to p=c(.8,.8) will find it

On 15/04/2008 6:59 PM, Bob Reilly wrote:
> The the use of optim with the L-BFGS-B method for the following simple 
> function gives erroneous results.  Any help appreciated!
> 
> Best,
> Bob Reilly
> 
> # Code:
> 
> V=function(p){
> p1=p[1];p2=p[2]
> y=p1*p2-.4*(p1+p2)
> return(-y)}
> 
> p=c(.2,.2) # p=c(.8,.8)
> 
> max=optim(p,V,method = "L-BFGS-B",lower=c(0,0),upper=c(1,1))
> max1=optim(max$par,V,method =
"L-BFGS-B",lower=c(0,0),upper=c(1,1))
> max2=optim(max1$par,V,method =
"L-BFGS-B",lower=c(0,0),upper=c(1,1))
> 
> max$par
> max1$par
> max2$par
> 
> -max2$value
> 
> -V(c(1,1)) # true maximum occurs at c(1,1)
> # setting the seed to p=c(.8,.8) will find it
The other starting value finds c(0,0) instead, and it's locally optimal. 
   optim() can't find global optima, only local ones.  When there are 
several local ones, the one it finds depends on where it starts.

Duncan Murdoch