[Ipopt] Ipopt Digest, Vol 66, Issue 8

[David Veerasingam]

You have a non-concave maximization problem with three stationarity  
points, and you're starting the solver on one of them. Being a local  
solver, all things being equal, it'll naturally converge on the  
closest point that satisfies optimality conditions. If you had started  
from x := 0.4999, you'd get a different answer.
	F = 1
	x = 0.146447

Also, your problem has non-unique global optima, so depending on where  
your initial guess is, you'll end up on one or the other.

Dave

>
> From: Paul Smith <phhs80 at gmail.com>
> Date: June 17, 2010 11:39:39 AM GMT-04:00
> To: ipopt mailing list <ipopt at list.coin-or.org>
> Subject: [Ipopt] A maximization problem returns a minimum
>
>
> 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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