[Coin-ipopt] Problems finding optimal solution to a rather small problem

[Uwe Kuessel]

Hello all,

i am working with IPOPT to solve a rather small optimization problem of
the following form:

min f(x) = (x3-x4)^2 + (x4-x5)^2

0 = A*3 - x1*x4 +A*x3
0 = B*3 - x2*x5 + B*x3
0 = B*3 - x3*x6 + C*x3 

0>=x1-x3
0>=x2-x3

0.1=<x1*x4=<0.35
0.1=<x2*x5=<0.35
0.1=<x3*x6=<0.35

6=<x1=<117
6=<x2=<117
6=<x3=<117

0.1/117=<x4=<0.35/6
0.1/117=<x5=<0.35/6
0.1/117=<x6=<0.35/6

[A B C]=[0.025 0.03 0.035] as an input to the system which might change
between two runs of IPOPT

and as starting point:

[x1 x2 x3 x4 x 5 x6]=[6 6.55 7 0.0416 0.0458 0.05]

I know that there is an optimal solution very close to the starting
point where x3=X4=x5 holds (coded an algorithm which tests for all
values of x1,x2,x3 in combination in the given bounds with a width of
0.01). Nevertheless the algorithm of IPOPT always converges to a point
where x1=x2=x3 as a local solution holds. I tested it for different
values of starting points and a variation of  [A B C] and always it runs
for x1=x2=x3. Even if  i change the objective function it comes up with
the same behaviour and always with an optimal solution. I add the
ipopt.out.

Has anyone an idea of what i did not consider? Or is the problem
statement wrong or in wrong formulation? Maybe some options i should
use?

thx

uwe
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