R help - Oct 2013 - Optimize function in R: unable to find maximum of logistic function

Hello Everyone,

I want to perform a 1-D optimization by using the optimize() function. I
want to find the maximum value of a "logistic" function. The
optimize()
function gives the wrong result.

My code:
f= function (k) {
T_s = 20
result = (2- 2/(1+ exp(-2*T_s*k)))
return(result)
}
optimize(f, c(0, 5), tol = 0.0000000000001, maximum= TRUE)

The maximum value for the function happens at k=0, and the maximum value is
1. Yet  the optimise function, says that the maximum value happens at k4.9995,
and the maximum value is 0.

Thanks in advance!

Warm Regards,
Shantanu

	[[alternative HTML version deleted]]

Hello,

This seems like a bug, removing 'maximum = TRUE' has no effect except 
that the returned value says it's a minimum, not a maximum.

Rui Barradas

Em 28-10-2013 17:00, Shantanu MULLICK escreveu:
> Hello Everyone,
>
> I want to perform a 1-D optimization by using the optimize() function. I
> want to find the maximum value of a "logistic" function. The
optimize()
> function gives the wrong result.
>
> My code:
> f= function (k) {
> T_s = 20
> result = (2- 2/(1+ exp(-2*T_s*k)))
> return(result)
> }
> optimize(f, c(0, 5), tol = 0.0000000000001, maximum= TRUE)
>
> The maximum value for the function happens at k=0, and the maximum value is
> 1. Yet  the optimise function, says that the maximum value happens at k>
4.9995, and the maximum value is 0.
>
> Thanks in advance!
>
> Warm Regards,
> Shantanu
>
> 	[[alternative HTML version deleted]]
>
> ______________________________________________
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> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

This could be described as a bug, perhaps.  Or it could be described as
an indication that numerical optimization is inevitably tricky. Notice that
if you narrow down your search interval from [0,5] to [0,0.5] you get the
right answer:

 > optimize(f, c(0, 0.5), maximum= TRUE,tol=1e-10)
$maximum
[1] 4.192436e-11

$objective
[1] 1

I guess there's a problem with finding a gradient that is effectively
(numerically) zero when "k" is equal to 5.


     cheers,

     Rolf Turner


On 10/29/13 06:00, Shantanu MULLICK wrote:
> Hello Everyone,
>
> I want to perform a 1-D optimization by using the optimize() function. I
> want to find the maximum value of a "logistic" function. The
optimize()
> function gives the wrong result.
>
> My code:
> f= function (k) {
> T_s = 20
> result = (2- 2/(1+ exp(-2*T_s*k)))
> return(result)
> }
> optimize(f, c(0, 5), tol = 0.0000000000001, maximum= TRUE)
>
> The maximum value for the function happens at k=0, and the maximum value is
> 1. Yet  the optimise function, says that the maximum value happens at k>
4.9995, and the maximum value is 0.
>