[Ipopt] Same initialization but different solutions (not the case with fmincon or KNitro)

[Arnaud Barré]

Hi,

I use Ipopt in Matlab and I have approximately the same results than fmincon (interior-point) or KNitro (direct).

I did a test where I run multiple times the same problem (i.e same initial conditions, same configurations) with the three algorithms. I have exactly the same results each time for fmincon and KNitro but not for Ipopt.

If I look in the output of Ipopt (print level 5), I can see a difference in the objective value after some iterations (see the end of this message for some examples). What could be the reason?

My problem is bound constrained only (as summarized below) using a monotone mu strategy, a partial derivate gradient approximation, a hessian approximation (limited-bfgs, max history 10) and the linear solver ma57. The other algorithms (fmincon, KNitro) are configured exactly with the same optons.

Thanks,

Arnaud

This is Ipopt version 3.11.0, running with linear solver ma57.

Number of nonzeros in equality constraint Jacobian...: 0
Number of nonzeros in inequality constraint Jacobian.: 0
Number of nonzeros in Lagrangian Hessian.............: 0

Total number of variables……………………….: 9
variables with only lower bounds: 0
variables with lower and upper bounds: 9
variables with only upper bounds: 0
Total number of equality constraints.................: 0
Total number of inequality constraints……………: 0
inequality constraints with only lower bounds: 0
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 0

------------------------------------------------------------------------------------
First 10 iterations / run #1
------------------------------------------------------------------------------------
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
   0  6.8420967e+03 0.00e+00 1.00e+02  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0
   1  4.9813866e+02 0.00e+00 3.67e+01  -1.0 4.35e+01    -  1.30e-02 2.21e-02f  1
   2  2.9178274e+02 0.00e+00 3.13e+01  -1.0 4.12e-01    -  8.23e-01 7.58e-01f  1
   3  1.5348471e+02 0.00e+00 1.85e+01  -1.0 8.93e-02    -  1.67e-01 1.00e+00f  1
   4  1.4216085e+02 0.00e+00 4.43e+00  -1.0 4.92e-02    -  9.90e-01 1.00e+00f  1
   5  1.3684436e+02 0.00e+00 1.89e+00  -1.0 2.75e-02    -  1.00e+00 1.00e+00f  1
   6  1.3270432e+02 0.00e+00 1.64e+00  -1.0 2.79e-02    -  1.00e+00 1.00e+00f  1
   7  9.0484123e+01 0.00e+00 4.07e+00  -1.0 2.08e-01    -  6.69e-01 1.00e+00f  1
   8  3.5107864e+01 0.00e+00 5.58e+00  -1.0 3.94e-01    -  1.00e+00 7.24e-01f  1
   9  4.3406913e+01 0.00e+00 8.46e+00  -1.0 5.44e-01    -  1.00e+00 2.50e-01f  3

------------------------------------------------------------------------------------
First 10 iterations / run #2 (the difference starts at the iteration 7)
------------------------------------------------------------------------------------
   0  6.8420967e+03 0.00e+00 1.00e+02  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0
   1  4.9813866e+02 0.00e+00 3.67e+01  -1.0 4.35e+01    -  1.30e-02 2.21e-02f  1
   2  2.9178274e+02 0.00e+00 3.13e+01  -1.0 4.12e-01    -  8.23e-01 7.58e-01f  1
   3  1.5348471e+02 0.00e+00 1.85e+01  -1.0 8.93e-02    -  1.67e-01 1.00e+00f  1
   4  1.4216085e+02 0.00e+00 4.43e+00  -1.0 4.92e-02    -  9.90e-01 1.00e+00f  1
   5  1.3684436e+02 0.00e+00 1.89e+00  -1.0 2.75e-02    -  1.00e+00 1.00e+00f  1
   6  1.3270432e+02 0.00e+00 1.64e+00  -1.0 2.79e-02    -  1.00e+00 1.00e+00f  1
   7  9.0484115e+01 0.00e+00 4.07e+00  -1.0 2.08e-01    -  6.69e-01 1.00e+00f  1
   8  3.5107870e+01 0.00e+00 5.58e+00  -1.0 3.94e-01    -  1.00e+00 7.24e-01f  1
   9  4.3406888e+01 0.00e+00 8.46e+00  -1.0 5.44e-01    -  1.00e+00 2.50e-01f  3