[R] optimize() stuck in local plateau ?

[Mike Lawrence]

Hi all,

Consider the following function:

####
my.func = function(x){
	y=ifelse(x>-.5,0,ifelse(x< -.8,abs(x)/2,abs(x)))
	print(c(x,y)) #print what was tested and what the result is
	return(y)
}
curve(my.func,from=-1,1)
####

When I attempt to find the maximum of this function, which should be  
-.8, I find that optimize gets stuck in the plateau area and doesn't  
bother testing the more interesting bits of the function:

####
optimize(my.func,interval=c(-1,1),maximum=TRUE)
####

I really don't understand why the search moves to the positive/ 
constant area of the function and neglects the more negative area of  
the function. On step #4, after finding that there is no difference  
between tests at -.23, .23 & .52, shouldn't the algorithm try -.52?  
In fact, it seems to me that it would make sense to try -.52 on step  
3, so that we've tested one negative, one positive (found no  
difference), now one negative again. Thoughts?

Of course I could define my interval more reasonably for this  
particular function, but this is in fact simply one of a class of  
functions I'm exploring, none of which have known formal descriptions  
as above (I'm exploring a large number of 'black boxes'). I do know  
that the maximum must occur between -1 and 1 for all however. Please  
advise on how I might use optimize more usefully.

Mike

--
Mike Lawrence
Graduate Student, Department of Psychology, Dalhousie University

Website: http://memetic.ca

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