[Ipopt] A maximization problem returns a minimum

[Andreas Waechter]

Hi Paul,

You give Ipopt x=0.5 as starting point.  At this point the KKT error is 
exactly zero, and Ipopt does not take any steps.  Ipopt is guaranteed only 
to find a first-order optimal point, and this is what it returns to you.

However, Ipopt has provisions that try to avoid a local maximizer, and if 
you just change the starting point a tiny bit to x=0.500001, it returns
x = 0.853553.

Hope this clarifies,

Andreas


On Thu, 17 Jun 2010, Paul Smith wrote:

> Dear All,
>
> I am running this simple model through AMPL and Ipopt 3.8.0:
>
> --------------------------------------
> var x >= 0;
>
> let x := 0.5;
>
> maximize F:
>   -16 * x * (x-1) * (2*x - 1)^2;
>
> subject to R1:
>   x <= 1;
> --------------------------------------
>
> Ipopt returns the following solution:
>
> «EXIT: Optimal Solution Found.
>
> Ipopt 3.8.0: Optimal Solution Found
>
> suffix ipopt_zU_out OUT;
> suffix ipopt_zL_out OUT;
> ampl: display F, x;
> F = 0
> x = 0.5».
>
> However the returned solution is a minimum and NOT a maximum. What am
> I not understanding?
>
> Thanks in advance,
>
> Paul
>
>
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