Again, it is not clear to me whether you are simply using MATPOWER’s OPF (i.e.
runopf) or implementing your own. It would seem you’re implementing your own
since the IPOPT output indicates that the Jacobian structure, Hessian and
Hessian structure are not supplied. With MATPOWER’s OPF implementation that
should not be the case. Here’s what I get …
>> mpopt = mpoption('out.all', 0, 'verbose', 2, 'opf.ac.solver', 'IPOPT');
>> runopf('case30', mpopt)
MATPOWER Version 5.1-dev, 06-Feb-2015 -- AC Optimal Power Flow
This is Ipopt version 3.10.3, running with linear solver mumps.
Number of nonzeros in equality constraint Jacobian...: 454
Number of nonzeros in inequality constraint Jacobian.: 324
Number of nonzeros in Lagrangian Hessian.............: 254
Total number of variables............................: 71
variables with only lower bounds: 0
variables with lower and upper bounds: 42
variables with only upper bounds: 0
Total number of equality constraints.................: 60
Total number of inequality constraints...............: 82
inequality constraints with only lower bounds: 0
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 82
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
0 4.9036963e+02 1.21e+00 1.06e+01 0.0 0.00e+00 - 0.00e+00 0.00e+00 0
1 5.2670003e+02 4.79e-01 1.87e+02 0.1 1.28e+00 - 3.77e-01 5.58e-01h 1
2 5.7233174e+02 1.44e-02 8.54e+01 -0.4 6.07e-01 - 1.00e+00 1.00e+00h 1
3 5.7307970e+02 1.39e-02 5.98e+01 -1.0 9.22e-02 - 9.99e-01 2.91e-01h 1
4 5.7635279e+02 5.84e-03 1.90e+02 -1.3 1.49e-01 - 1.00e+00 1.00e+00h 1
5 5.7698733e+02 9.81e-04 6.93e+00 -2.0 6.20e-02 - 1.00e+00 1.00e+00h 1
6 5.7693657e+02 7.09e-05 5.84e+00 -2.9 1.30e-02 - 1.00e+00 1.00e+00h 1
7 5.7689674e+02 1.42e-05 6.89e-01 -3.8 7.65e-03 - 1.00e+00 1.00e+00h 1
8 5.7689223e+02 9.17e-06 5.46e-02 -5.3 6.06e-03 - 1.00e+00 1.00e+00h 1
9 5.7689227e+02 1.58e-06 1.08e-02 -6.8 2.65e-03 - 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
10 5.7689232e+02 2.06e-07 1.63e-03 -8.3 9.69e-04 - 1.00e+00 1.00e+00h 1
11 5.7689233e+02 1.32e-08 1.19e-04 -9.3 2.47e-04 - 1.00e+00 1.00e+00h 1
12 5.7689233e+02 1.13e-10 1.08e-06 -11.0 2.29e-05 - 1.00e+00 1.00e+00h 1
13 5.7689233e+02 1.36e-14 9.86e-11 -11.0 2.15e-07 - 1.00e+00 1.00e+00h 1
Number of Iterations....: 13
(scaled) (unscaled)
Objective...............: 1.3985268672263120e+02 5.7689233273085370e+02
Dual infeasibility......: 9.8586584428882276e-11 4.0666966076913940e-10
Constraint violation....: 1.3558539391522494e-14 1.3558539391522494e-14
Complementarity.........: 1.0529404232602505e-11 4.3433792459485328e-11
Overall NLP error.......: 9.8586584428882276e-11 4.0666966076913940e-10
Number of objective function evaluations = 14
Number of objective gradient evaluations = 14
Number of equality constraint evaluations = 14
Number of inequality constraint evaluations = 14
Number of equality constraint Jacobian evaluations = 14
Number of inequality constraint Jacobian evaluations = 14
Number of Lagrangian Hessian evaluations = 13
Total CPU secs in IPOPT (w/o function evaluations) = 0.035
Total CPU secs in NLP function evaluations = 0.046
EXIT: Optimal Solution Found.
>>
Regarding the issue of the objective function decreasing with each iteration,
that is not necessarily to be expected with primal-dual interior point solvers
such as the one used by IPOPT. The objective function may need to increase in
order to improve feasibility.
Ray
> On Feb 14, 2015, at 2:33 PM, Bouchekara Houssem
> <[email protected]> wrote:
>
> Dear all
> I am trying to solve the OPF using the IPOPT solver (application on the IEEE
> 30 bus test system).
> However, I have some issues.
>
> The first one is that this solver takes many iterations and at the end, I
> receive the message "Maximum Number of Iterations Exceeded.". if I increase
> the number of iterations I obtain the same message on the time of simulation
> !!!
>
> The second issue or question is that the objective function keep changing but
> not always decreasing as you can see in the herewith results. I have run the
> same problem using the fmincon function the objective function does not
> increase at all it decreases all the time until convergence !!!
>
> Regards
>
>
> Results
> %-------------------------------------------------------------------------------------------------------------------
> ------------------------------------------------------
> Nonlinear Program (NLP) Optimization
> min f(x)
> s.t. lb <= x <= ub
> cl <= c(x) <= cu
> ------------------------------------------------------
> Problem Properties:
> # Decision Variables: 24
> # Constraints: 233
> # Bounds: 48
> # Nonlinear Inequality: 185
> ------------------------------------------------------
> Solver Parameters:
> Solver: IPOPT
> Objective Gradient: @(x)mklJac(prob.fun,x,1) [numdiff]
> Constraint Jacobian: @(x)mklJac(prob.nlcon,x,nnl) [numdiff]
> Jacobian Structure: Not Supplied
> Lagrangian Hessian: Not Supplied
> Hessian Structure: Not Supplied
> ------------------------------------------------------
>
> ******************************************************************************
> This program contains Ipopt, a library for large-scale nonlinear optimization.
> Ipopt is released as open source code under the Eclipse Public License (EPL).
> For more information visit http://projects.coin-or.org/Ipopt
> <http://projects.coin-or.org/Ipopt>
> ******************************************************************************
>
> This is Ipopt version 3.11.7, running with linear solver ma57.
>
> Number of nonzeros in equality constraint Jacobian...: 0
> Number of nonzeros in inequality constraint Jacobian.: 2712
> Number of nonzeros in Lagrangian Hessian.............: 0
>
> Total number of variables............................: 24
> variables with only lower bounds: 0
> variables with lower and upper bounds: 24
> variables with only upper bounds: 0
> Total number of equality constraints.................: 0
> Total number of inequality constraints...............: 113
> inequality constraints with only lower bounds: 0
> inequality constraints with lower and upper bounds: 72
> inequality constraints with only upper bounds: 41
>
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr
> ls
> 0 8.2505796e+002 3.92e+001 2.39e+000 0.0 0.00e+000 - 0.00e+000
> 0.00e+000 0
> 1 8.2333913e+002 3.43e+001 2.88e+001 0.0 3.26e+000 - 4.40e-001
> 7.91e-002f 2
> 2 8.1521317e+002 0.00e+000 6.48e+001 -0.4 5.64e+000 - 8.84e-001
> 1.00e+000f 1
> 3 8.0493896e+002 0.00e+000 6.52e+001 0.0 3.96e+001 - 8.87e-001
> 4.80e-001f 2
> 4 8.0277302e+002 0.00e+000 2.39e+001 -0.1 3.95e+000 - 9.88e-001
> 1.00e+000h 1
> 5 8.0079336e+002 0.00e+000 3.27e+001 -0.8 5.65e+000 - 9.86e-001
> 1.00e+000f 1
> 6 7.9975232e+002 0.00e+000 1.50e+001 -1.3 1.64e+000 - 9.99e-001
> 7.80e-001f 1
> 7 7.9977509e+002 0.00e+000 1.70e+001 -1.1 1.52e+000 - 1.00e+000
> 1.00e+000h 1
> 8 7.9947341e+002 0.00e+000 2.73e+000 -1.7 7.49e-001 - 9.98e-001
> 1.00e+000h 1
> 9 7.9933411e+002 0.00e+000 1.06e+001 -2.2 2.68e+000 - 9.99e-001
> 1.00e+000h 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr
> ls
> 10 7.9931298e+002 0.00e+000 1.50e+001 -1.9 4.96e+000 - 1.00e+000
> 1.00e+000H 1
> 11 7.9945021e+002 0.00e+000 2.00e+001 -1.6 9.10e+000 - 1.00e+000
> 4.53e-001f 2
> 12 7.9940918e+002 0.00e+000 5.80e+000 -1.7 2.61e+000 - 7.69e-001
> 1.00e+000h 1
> 13 7.9935727e+002 0.00e+000 9.48e+000 -1.7 5.58e+000 - 8.33e-001
> 2.62e-001h 2
> 14 7.9970882e+002 0.00e+000 1.04e+001 -1.7 4.50e+000 - 1.00e+000
> 1.00e+000H 1
> 15 7.9936389e+002 0.00e+000 1.04e+001 -1.7 3.89e+000 - 1.00e+000
> 1.00e+000H 1
> 16 7.9932908e+002 0.00e+000 2.52e+000 -1.7 1.06e+001 - 5.30e-001
> 8.14e-002h 3
> 17 7.9940245e+002 0.00e+000 9.01e+000 -1.7 9.80e-001 - 1.00e+000
> 1.00e+000h 1
> 18 8.0110400e+002 0.00e+000 2.25e+001 -1.7 1.04e+001 - 5.27e-001
> 1.00e+000H 1
> 19 7.9946399e+002 0.00e+000 4.25e+000 -1.7 1.20e+001 - 1.00e+000
> 1.00e+000F 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr
> ls
> 20 7.9948550e+002 0.00e+000 1.00e+001 -1.3 1.24e+001 - 1.00e+000
> 2.28e-001f 2
> 21 7.9975197e+002 0.00e+000 1.65e+001 -1.5 3.80e+000 - 7.44e-001
> 1.00e+000h 1
> 22 8.0029390e+002 0.00e+000 4.95e+001 -1.5 4.78e+000 - 1.00e+000
> 7.66e-001H 1
> 23 7.9969885e+002 0.00e+000 3.75e+001 -1.5 7.79e+000 - 4.43e-001
> 7.55e-001F 1
> 24 8.0153952e+002 0.00e+000 5.42e+001 -1.5 6.09e+000 - 3.71e-001
> 1.00e+000H 1
> 25 8.0083849e+002 0.00e+000 5.53e+001 -1.5 9.48e+000 - 3.14e-001
> 1.60e-001f 3
> 26 8.0055898e+002 0.00e+000 5.68e+001 -1.5 7.24e+001 - 1.35e-001
> 2.09e-002f 3
> 27 7.9993130e+002 0.00e+000 2.14e+001 -1.5 1.56e+001 - 1.22e-001
> 1.16e-001f 2
> 28 7.9966609e+002 0.00e+000 2.34e+001 -1.5 1.13e+001 - 1.91e-001
> 2.55e-001h 1
> 29 7.9951187e+002 0.00e+000 4.68e+000 -1.5 1.61e+001 - 7.25e-002
> 2.62e-001f 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr
> ls
> 30 8.0267261e+002 0.00e+000 2.31e+001 -1.5 9.14e+000 - 6.12e-001
> 9.49e-001H 1
> 31 8.0226367e+002 0.00e+000 1.04e+001 -1.5 1.01e+001 - 3.30e-001
> 8.99e-002f 3
> 32 8.0192666e+002 0.00e+000 1.32e+001 -1.5 2.47e+001 - 8.06e-002
> 2.93e-002f 4
> 33 8.0132986e+002 0.00e+000 9.01e+000 -1.5 1.40e+001 - 5.76e-001
> 1.32e-001f 1
> 34 8.0105092e+002 0.00e+000 6.84e+000 -1.5 7.34e+000 - 8.30e-001
> 9.60e-002f 3
> 35 7.9977021e+002 0.00e+000 3.28e+001 -1.5 9.26e+000 - 3.27e-001
> 8.37e-001F 1
> 36 8.0033089e+002 0.00e+000 4.86e+001 -1.5 4.62e+000 - 1.00e+000
> 1.00e+000H 1
> 37 7.9996104e+002 0.00e+000 1.06e+001 -1.5 5.43e+000 - 1.96e-001
> 1.75e-001f 2
> 38 7.9951421e+002 0.00e+000 9.42e+000 -1.5 1.59e+001 - 2.53e-001
> 1.96e-001f 2
> 39 7.9967929e+002 0.00e+000 3.01e+001 -1.5 3.16e+000 - 9.19e-001
> 7.79e-001H 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr
> ls
> 40 7.9962530e+002 0.00e+000 2.19e+001 -1.5 6.91e+000 - 1.80e-001
> 1.78e-001h 3
> 41 7.9951740e+002 0.00e+000 1.26e+000 -1.5 1.88e+000 - 1.00e+000
> 1.00e+000h 1
> 42 8.0007055e+002 0.00e+000 9.26e+000 -1.5 3.65e+000 - 1.00e+000
> 1.00e+000H 1
> 43 7.9994265e+002 0.00e+000 7.74e+000 -1.5 7.16e+000 - 5.93e-001
> 9.68e-002h 4
> 44 7.9969538e+002 0.00e+000 6.51e+000 -1.5 7.45e+000 - 6.32e-001
> 1.92e-001h 2
> 45 7.9957525e+002 0.00e+000 4.13e+000 -1.5 1.30e+001 - 4.92e-001
> 5.31e-002h 3
> 46 7.9993363e+002 0.00e+000 2.71e+001 -1.5 4.17e+000 - 4.89e-001
> 1.00e+000H 1
> 47 7.9973977e+002 0.00e+000 1.60e+001 -1.5 5.74e+000 - 6.88e-001
> 3.02e-001h 2
> 48 7.9989765e+002 0.00e+000 2.33e+001 -1.5 4.88e+000 - 1.00e+000
> 1.00e+000H 1
> 49 7.9983511e+002 0.00e+000 2.31e+001 -1.5 1.74e+001 - 6.39e-001
> 5.01e-002h 5
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr
> ls
> 50 7.9970425e+002 0.00e+000 1.59e+001 -1.5 2.09e+001 - 2.33e-001
> 8.10e-002h 3
> 51 7.9955418e+002 0.00e+000 5.09e+000 -1.5 1.94e+001 - 2.51e-001
> 6.63e-002f 2
> 52 7.9950139e+002 0.00e+000 3.11e+000 -1.5 6.47e+000 - 4.13e-001
> 8.04e-002h 4
> 53 7.9944413e+002 0.00e+000 1.92e+000 -1.5 3.36e+000 - 8.24e-001
> 2.06e-001h 3
> 54 8.0126819e+002 0.00e+000 3.56e+001 -1.5 8.76e+000 - 6.44e-001
> 1.00e+000H 1
> 55 7.9945686e+002 0.00e+000 2.26e+000 -1.5 9.10e+000 - 1.00e+000
> 1.00e+000F 1
> 56 7.9950057e+002 0.00e+000 1.04e+001 -1.5 1.95e+000 - 1.00e+000
> 1.00e+000H 1
> 57 7.9942217e+002 0.00e+000 1.84e+001 -1.7 1.70e+000 - 1.00e+000
> 1.00e+000h 1
> 58 8.0023640e+002 0.00e+000 6.79e+001 -1.8 2.88e+000 - 2.83e-001
> 1.00e+000H 1
> 59 8.0004652e+002 0.00e+000 5.87e+001 -1.8 6.11e+000 - 5.91e-001
> 9.88e-002h 4
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr
> ls
> 60 7.9981714e+002 0.00e+000 5.01e+001 -1.8 2.04e+001 - 7.88e-002
> 4.40e-002f 4
> 61 7.9975653e+002 0.00e+000 4.73e+001 -1.8 9.31e+000 - 8.23e-001
> 2.59e-002h 4
> 62 7.9970454e+002 0.00e+000 4.19e+001 -1.8 3.96e+000 - 4.82e-001
> 3.85e-002h 5
> 63 7.9962939e+002 0.00e+000 3.88e+001 -1.8 4.97e+000 - 2.21e-001
> 5.05e-002h 5
> 64 7.9953788e+002 0.00e+000 3.19e+001 -1.8 1.07e+001 - 3.03e-001
> 1.32e-001h 2
> 65 7.9939133e+002 0.00e+000 1.33e+001 -1.8 1.27e+001 - 2.71e-001
> 1.24e-001h 2
> 66 7.9939690e+002 0.00e+000 4.01e+000 -1.8 7.99e+000 - 3.71e-001
> 4.06e-001h 2
> 67 7.9936697e+002 0.00e+000 4.73e+000 -1.8 4.44e+001 - 3.91e-001
> 3.41e-002h 4
> 68 7.9936784e+002 0.00e+000 1.89e+000 -1.8 1.39e+001 - 9.19e-001
> 1.23e-001h 4
> 69 7.9943394e+002 0.00e+000 1.13e+001 -1.8 7.41e+000 - 3.90e-001
> 3.38e-001w 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr
> ls
> 70 8.0333982e+002 3.88e-001 6.64e+001 -1.8 1.21e+001 - 4.03e-001
> 9.33e-001w 1
> 71 8.0004084e+002 2.01e+000 2.23e+001 -1.8 9.50e+000 - 1.75e-001
> 8.22e-001w 1
> 72 7.9932137e+002 0.00e+000 4.72e+000 -1.8 8.14e+001 - 3.90e-001
> 1.69e-001h 1
> 73 7.9933546e+002 0.00e+000 1.20e+001 -1.8 2.20e+000 - 1.00e+000
> 4.15e-001h 2
> 74 7.9930951e+002 0.00e+000 8.03e+000 -1.8 2.31e+001 - 2.28e-001
> 5.44e-002h 4
> 75 8.0016365e+002 0.00e+000 6.14e+001 -1.9 2.00e+000 - 9.59e-001
> 1.00e+000H 1
> 76 7.9955770e+002 0.00e+000 4.24e+001 -2.0 5.35e+000 - 7.40e-001
> 4.29e-001f 1
> 77 7.9939342e+002 0.00e+000 1.45e+001 -2.0 2.40e+001 - 1.52e-001
> 9.57e-002h 2
> 78 7.9925263e+002 0.00e+000 1.21e+001 -2.0 1.69e+001 - 1.18e-001
> 1.51e-001h 2
> 79 7.9941302e+002 0.00e+000 1.24e+001 -1.3 1.89e+001 - 9.77e-001
> 1.77e-001h 2
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr
> ls
> 80 8.0134560e+002 0.00e+000 3.00e+001 -1.4 4.81e+000 - 6.41e-001
> 1.00e+000h 1
> 81 7.9998500e+002 0.00e+000 1.73e+001 -1.4 7.31e+000 - 9.05e-001
> 8.39e-001f 1
> 82 7.9953189e+002 0.00e+000 4.34e+000 -1.4 2.20e+001 - 7.03e-001
> 1.77e-001f 2
> 83 7.9959732e+002 0.00e+000 1.07e+001 -1.4 3.78e+000 - 6.33e-001
> 1.00e+000h 1
> 84 8.0004713e+002 0.00e+000 3.44e+001 -1.4 4.05e+000 - 1.00e+000
> 1.00e+000H 1
> 85 7.9988950e+002 0.00e+000 3.31e+001 -1.4 3.13e+001 - 5.62e-001
> 9.57e-002f 2
> 86 7.9955465e+002 0.00e+000 1.76e+001 -1.4 1.50e+000 - 1.00e+000
> 1.00e+000h 1
> 87 7.9949662e+002 0.00e+000 7.54e+000 -1.4 3.70e+000 - 2.85e-001
> 1.85e-001h 3
> 88 7.9959288e+002 0.00e+000 1.71e+001 -1.4 1.39e+000 - 1.00e+000
> 1.00e+000h 1
> 89 8.0006272e+002 0.00e+000 1.37e+001 -1.4 5.26e+000 - 1.00e+000
> 1.00e+000h 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr
> ls
> 90 7.9980392e+002 0.00e+000 1.44e+001 -1.4 6.97e+000 - 4.93e-001
> 2.01e-001h 2
> 91 7.9963251e+002 0.00e+000 8.20e+000 -1.4 9.82e+000 - 5.22e-001
> 1.65e-001h 3
> 92 7.9959672e+002 0.00e+000 2.45e+000 -1.4 3.24e+001 - 7.30e-001
> 1.55e-001h 2
> 93 7.9951429e+002 0.00e+000 3.42e+000 -1.4 3.75e+000 - 8.01e-001
> 1.00e+000h 1
> 94 7.9972009e+002 0.00e+000 1.76e+001 -1.4 2.53e+000 - 1.00e+000
> 1.00e+000H 1
> 95 7.9971154e+002 0.00e+000 2.36e+001 -1.4 2.37e+000 - 7.73e-001
> 1.00e+000H 1
> 96 7.9958228e+002 0.00e+000 1.80e+001 -1.4 1.65e+001 - 4.70e-001
> 1.12e-001h 2
> 97 7.9950114e+002 0.00e+000 7.95e+000 -1.4 3.83e+000 - 1.00e+000
> 2.99e-001h 2
> 98 7.9964810e+002 0.00e+000 1.43e+001 -1.4 2.33e+000 - 9.82e-001
> 1.00e+000H 1
> 99 7.9958083e+002 0.00e+000 9.04e+000 -1.4 2.42e+000 - 1.00e+000
> 1.00e+000H 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr
> ls
> 100 7.9957133e+002 0.00e+000 5.14e+000 -1.4 1.19e+001 - 4.74e-001
> 1.06e-001h 3
>
> Number of Iterations....: 100
>
> (scaled) (unscaled)
> Objective...............: 7.9957132849034247e+002 7.9957132849034247e+002
> Dual infeasibility......: 5.1351489054861581e+000 5.1351489054861581e+000
> Constraint violation....: 0.0000000000000000e+000 0.0000000000000000e+000
> Complementarity.........: 6.3178225777153776e-002 6.3178225777153776e-002
> Overall NLP error.......: 5.1351489054861581e+000 5.1351489054861581e+000
>
>
> Number of objective function evaluations = 331
> Number of objective gradient evaluations = 101
> Number of equality constraint evaluations = 0
> Number of inequality constraint evaluations = 331
> Number of equality constraint Jacobian evaluations = 0
> Number of inequality constraint Jacobian evaluations = 101
> Number of Lagrangian Hessian evaluations = 0
> Total CPU secs in IPOPT (w/o function evaluations) = 2.533
> Total CPU secs in NLP function evaluations = 125.944
>
> EXIT: Maximum Number of Iterations Exceeded.
> %-------------------------------------------------------------------------------------------------------------------
