Minimization problem

[sferrera]

Dear Anders

I am trying to minimize the 1D polynomial f(x) = x + x2/2 under the
constraints -10<x<10 and with initial guess x = 1.
Accordingly the gradient is g(x) = 1 + x and the hessian h(x) = 1.
IPopt fails to find the minimum x=-1/4 as the iterations deviate only
marginally from the initial value as shown:

iter objective inf_pr inf_du
lg(mu) || d || lg(rg) alpha_du alpha_pr ls
0 1,5000000e+000 0,00e+000 0,00e+000 0 0,00e+000
- 0,00e+000 0,00e+000 0
1 1,5000000e+000 0,00e+000 3,98e-012 0 4,00e-012
- 9,90e-001 1,00e+000f 1
2 1,4999999e+000 0,00e+000 3,20e-008 3,9 3,20e-008
- 1,00e+000 1,00e+000f 1
3 1,4999999e+000 0,00e+000 6,40e-009 3,2 6,40e-009
- 1,00e+000 1,00e+000f 1
4 1,4999999e+000 0,00e+000 1,28e-009 2,5 1,28e-009
- 1,00e+000 1,00e+000f 1
5 1,4999999e+000 0,00e+000 2,56e-010 1,8 2,56e-010
- 1,00e+000 1,00e+000f 1
6 1,4999999e+000 0,00e+000 5,12e-011 1,1 5,12e-011
- 1,00e+000 1,00e+000f 1
7 1,4999999e+000 0,00e+000 1,02e-011 0,4 1,02e-011
- 1,00e+000 1,00e+000f 1
8 1,4999999e+000 0,00e+000 2,05e-012 -0,3 2,05e-012
- 1,00e+000 1,00e+000f 1
9 1,4999999e+000 0,00e+000 4,10e-013 -1 4,10e-013
- 1,00e+000 1,00e+000f 1
10 1,4999999e+000 0,00e+000 8,19e-014 -1,7 8,19e-014
- 1,00e+000 1,00e+000f 1
11 1,4999999e+000 0,00e+000 1,17e-014 -2,5 1,17e-014
- 1,00e+000 1,00e+000f 1
12 1,4999999e+000 0,00e+000 1,72e-017 -8,5 1,17e-020
- 9,97e-001 1,00e+000 0
13 1,4999999e+000 0,00e+000 2,75e-017 -5,2 2,75e-017
- 1,00e+000 1,00e+000T 0
14 1,4999999e+000 0,00e+000 7,21e-020 -7,7 7,21e-020
- 1,00e+000 1,00e+000T 0


Please advise me how to proceed. I suspect this must be a minor option
setting.

Thank you.

Sebastian.

[Anders Gustafsson (Cureos AB)]

Dear Sebastian,

sorry for not having responded any earlier. However, if I understand
correctly, you have received sufficient help with this problem from
the main Ipopt forum, right?
http://list.coin-or.org/pipermail/ipopt/2010-December/002229.html

If not, please let me know.

Best regards,
Anders

[sferrera]

Dear Anders,

You're right, I received a lot of help but I can't find a solution
yet... I think the problem is allocated on my eval functions, is that
possible?

Best regards,

Sebastian.



On 11 dic, 16:46, "Anders Gustafsson (Cureos AB)" <and...@cureos.com>
wrote:

> Dear Sebastian,
>
> sorry for not having responded any earlier. However, if I understand
> correctly, you have received sufficient help with this problem from

> the main Ipopt forum, right?http://list.coin-or.org/pipermail/ipopt/2010-December/002229.html

[Anders Gustafsson (Cureos AB)]

Dear Sebastian,

could you please provide the detailed problem formulation? I am not
sure that I understand what you mean with your reply on the Ipopt
forum: "I am using the same boundary condition on x twice: first as
-10 < x < 10 and then as -10 < f(x) = x < 10"? Does this mean that you
are actually trying to solve the equation x = x + x2/2 with Ipopt?

Regards,
Anders