# [Coin-ipopt] Unconstrained optimization

Andreas Waechter andreasw at watson.ibm.com
Tue Jun 28 16:27:12 EDT 2005

```Hi Andrew,

I just tried the AMPL formulation of your problem on NEOS

(see http://www-neos.mcs.anl.gov/neos/solvers/NCO:IPOPT )

---- 8< ----------------------------

var x{1..3};

minimize f: 100*(x[2] - x[1]^2)^2 + (1 - x[1])^2;

subject to

lin:    x[1] + x[2] - x[3] = 0;

data;

# starting point
let x[1] := -1.2;
let x[2] := 1.0;
let x[3] := -0.2;

option presolve 0;

---- 8< ----------------------------

It seems to work fine and is solved with optimal final objective function
essentially zero.

You probably didn't use AMPL and might have a bug in your problem
formulation code (computing values and derivatives of the objective
function or constraints...) or in your interface to the Ipopt library.

By the way, technically speaking, your problem is not unconstrained, since
you have an equality constraint.  However, that constraint doesn't really
do anything expect defining x3 (which does not appear in the objective).
The problem is the same as if you would get rid of the constraint (which
then would be an unconstrained problem).

There is no reason why Ipopt should not work for unconstrained problems.
The test set used in the paper describing the Ipopt algorithm contains
many unconstrained problems.

Regards,

Andreas

On Tue, 28 Jun 2005, Andrew Lambe wrote:

> Hi,
>
> I am currently testing IPOPT with the following (unconstrained) optimization
> problem:
>
> C***********************************************
> C    	min      100*(x2 - x1^2)^2 + (1 - x1)^2
> C
> C	s.t.	x1 + x2 - x3 = 0
> C
> C     Starting point:
> C        x = (-1.2, 1.0, -0.2)
> C***********************************************
>
> where x3 is a slack variable and its bounds are defined as -1.d20 and 1.d20,
> with x1 and x2 unbounded. Every time I run this problem, regardless of choice of
> starting point or bounds on x3, I either get error 1 or error 18. I just wanted
> to know if IPOPT is able to work with unconstrained optimization at all. Thanks.
>
> Andrew Lambe
> Summer Student
> University of Toronto Institute for Aerospace Studies (UTIAS)
>
> _______________________________________________
> Coin-ipopt mailing list
> Coin-ipopt at list.coin-or.org
> http://list.coin-or.org/mailman/listinfo/coin-ipopt
>

```