[R] disturbing seed dependence in optim L-BFGS-B method

[Duncan Murdoch]

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