# Long NLP evaluation time in Ipopt
**URL:** https://discourse.julialang.org/t/long-nlp-evaluation-time-in-ipopt/109436
**Category:** Optimization (Mathematical)
**Tags:** question, jump, ipopt
**Created:** [January 30, 2024, 8:56am UTC](https://discourse.julialang.org/t/long-nlp-evaluation-time-in-ipopt/109436 "2024-01-30T08:56:53Z")
**Posts on this page:** 7
**Page:** 1
### Author:  [@tso-martin](https://discourse.julialang.org/u/tso-martin)
#### Post date: [January 30, 2024, 8:56am UTC](https://discourse.julialang.org/t/long-nlp-evaluation-time-in-ipopt/109436/1 "2024-01-30T08:56:53Z")
Dear all,
I encounter long evaluation times and slow convergence in an AC security constraint optimal power flow (SCOPF) optimization. The problem is modelled with PowerModels and JuMP. The NLP evaluation time is higher than the time for Ipopt itself.
```julia
Total seconds in IPOPT (w/o function evaluations) = 61.769
Total seconds in NLP function evaluations = 69.785
```
Are there any suggestions or indications on how to improve the performance of the solving process? Your help is highly appreciated.
Below you will find the Ipopt log:
```julia
List of user-set options:
Name Value used
acceptable_iter = 5 yes
acceptable_tol = 0.1 yes
check_derivatives_for_naninf = yes yes
compl_inf_tol = 0.001 yes
constr_viol_tol = 0.01 yes
hsllib = \HSL\JuliaHSL\lbt_HSL_jll.jl-2023.5.26\HSL_jll.jl-2023.5.26\override\bin\x86_64-w64-mingw32-libgfortran5\libhsl.dll yes
linear_solver = ma57 yes
max_iter = 700 yes
obj_scaling_factor = 1 yes
print_level = 5 yes
print_timing_statistics = yes yes
print_user_options = yes yes
tol = 0.01 yes
warm_start_init_point = yes yes
This is Ipopt version 3.14.13, running with linear solver ma57.
Number of nonzeros in equality constraint Jacobian...: 250815
Number of nonzeros in inequality constraint Jacobian.: 41004
Number of nonzeros in Lagrangian Hessian.............: 371090
Total number of variables............................: 73711
variables with only lower bounds: 1584
variables with lower and upper bounds: 26292
variables with only upper bounds: 1584
Total number of equality constraints.................: 70747
Total number of inequality constraints...............: 27608
inequality constraints with only lower bounds: 0
inequality constraints with lower and upper bounds: 0
inequality constraints with only upper bounds: 27608
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
0 9.1716842e+01 9.38e+00 3.00e+01 -1.0 0.00e+00 - 0.00e+00 0.00e+00 0
Reallocating memory for MA57: lfact (4602841)
1 4.3180404e+01 9.38e+00 3.00e+01 -1.0 1.16e+02 -2.0 6.01e-04 1.33e-04f 1
2 1.8568919e+02 9.36e+00 2.99e+01 -1.0 6.42e+01 -1.6 2.85e-03 2.60e-03f 1
3 1.1234750e+02 9.32e+00 2.98e+01 -1.0 9.91e+00 -0.2 4.61e-03 4.05e-03f 1
4 1.1873445e+02 9.27e+00 2.97e+01 -1.0 9.95e+00 0.2 4.28e-03 5.81e-03f 1
5 1.2573785e+02 9.23e+00 2.95e+01 -1.0 1.02e+01 0.6 8.90e-03 4.07e-03f 1
6 1.5780528e+02 9.06e+00 2.90e+01 -1.0 1.00e+01 0.1 1.58e-02 1.86e-02f 1
7 1.6383345e+02 9.03e+00 2.90e+01 -1.0 9.97e+00 0.6 1.59e-02 2.84e-03f 1
8 1.7170531e+02 9.00e+00 2.89e+01 -1.0 1.00e+01 1.0 1.71e-02 3.39e-03f 1
9 2.0612521e+02 8.86e+00 2.85e+01 -1.0 9.95e+00 0.5 2.41e-02 1.53e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
10 2.2128040e+02 8.81e+00 2.83e+01 -1.0 9.85e+00 0.9 2.32e-02 6.20e-03f 1
11 2.8837520e+02 8.55e+00 2.74e+01 -1.0 9.76e+00 0.5 3.33e-02 2.88e-02f 1
12 3.2302020e+02 8.44e+00 2.70e+01 -1.0 9.52e+00 0.9 9.33e-03 1.40e-02f 1
13 3.4104303e+02 8.37e+00 2.68e+01 -1.0 9.40e+00 1.3 1.83e-02 7.22e-03f 1
14 4.1952990e+02 8.11e+00 3.23e+01 -1.0 9.33e+00 0.8 1.02e-01 3.18e-02f 1
15 5.3188049e+02 7.70e+00 3.32e+01 -1.0 8.98e+00 0.4 1.38e-01 5.05e-02f 1
16 5.3755905e+02 7.68e+00 5.65e+01 -1.0 8.56e+00 0.8 1.59e-01 2.48e-03f 1
17 6.3886075e+02 7.30e+00 5.21e+01 -1.0 8.58e+00 0.3 2.03e-01 4.92e-02f 1
18 6.9565220e+02 7.11e+00 5.44e+01 -1.0 8.25e+00 0.7 5.37e-02 2.65e-02f 1
19 7.9883169e+02 6.71e+00 5.45e+01 -1.0 8.13e+00 0.2 1.47e-01 5.67e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
20 8.4943970e+02 6.53e+00 5.10e+01 -1.0 7.74e+00 0.7 1.57e-02 2.63e-02f 1
21 9.1263316e+02 6.27e+00 4.90e+01 -1.0 7.55e+00 0.2 3.79e-02 4.00e-02f 1
22 9.6314034e+02 6.09e+00 4.62e+01 -1.0 7.28e+00 0.6 1.98e-02 2.87e-02f 1
23 9.8303312e+02 6.02e+00 5.00e+01 -1.0 7.10e+00 1.0 1.92e-02 1.09e-02f 1
24 1.0224924e+03 5.88e+00 5.22e+01 -1.0 7.01e+00 0.6 5.63e-02 2.42e-02f 1
25 1.0379435e+03 5.82e+00 5.12e+01 -1.0 6.84e+00 1.0 8.01e-03 9.19e-03f 1
26 1.0558877e+03 5.75e+00 5.15e+01 -1.0 6.72e+00 0.5 2.39e-02 1.18e-02f 1
27 1.1105068e+03 5.56e+00 4.64e+01 -1.0 6.66e+00 0.9 2.39e-02 3.35e-02f 1
28 1.2114942e+03 5.17e+00 4.11e+01 -1.0 6.43e+00 0.5 1.62e-02 7.08e-02f 1
29 1.2272061e+03 5.11e+00 5.05e+01 -1.0 6.02e+00 0.9 4.90e-02 1.09e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
30 1.2406552e+03 5.06e+00 5.86e+01 -1.0 5.92e+00 0.4 4.95e-02 1.06e-02f 1
31 1.2849234e+03 4.89e+00 4.54e+01 -1.0 5.89e+00 0.8 1.77e-02 3.20e-02f 1
32 1.3198929e+03 4.75e+00 4.43e+01 -1.0 5.66e+00 0.4 1.89e-02 2.93e-02f 1
33 1.3553176e+03 4.62e+00 4.25e+01 -1.0 5.54e+00 0.8 2.31e-02 2.75e-02f 1
34 1.4023239e+03 4.42e+00 3.76e+01 -1.0 5.34e+00 0.3 1.12e-01 4.23e-02f 1
35 1.4079102e+03 4.40e+00 6.36e+01 -1.0 5.16e+00 0.7 4.34e-02 4.61e-03h 1
36 1.4433519e+03 4.28e+00 3.31e+01 -1.0 5.16e+00 1.2 1.30e-02 2.78e-02h 1
37 1.4790161e+03 4.15e+00 4.01e+01 -1.0 5.00e+00 0.7 4.51e-02 3.05e-02f 1
38 1.5041851e+03 4.07e+00 3.86e+01 -1.0 4.86e+00 1.1 2.02e-02 2.06e-02h 1
39 1.5323190e+03 3.96e+00 5.45e+01 -1.0 4.74e+00 0.6 6.91e-02 2.54e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
40 1.5474848e+03 3.91e+00 5.34e+01 -1.0 4.64e+00 1.1 1.36e-02 1.38e-02h 1
41 1.5985807e+03 3.71e+00 5.11e+01 -1.0 4.58e+00 0.6 5.34e-02 5.16e-02f 1
42 1.6230259e+03 3.62e+00 1.12e+02 -1.0 4.37e+00 1.0 5.13e-02 2.42e-02h 1
43 1.7076968e+03 3.27e+00 1.27e+02 -1.0 4.26e+00 0.5 1.72e-01 9.47e-02f 1
44 1.7112064e+03 3.26e+00 2.51e+02 -1.0 3.87e+00 1.0 7.43e-02 3.92e-03h 1
45 1.7593780e+03 3.06e+00 2.34e+02 -1.0 3.85e+00 0.5 1.28e-01 6.04e-02f 1
46 1.7665410e+03 3.04e+00 2.38e+02 -1.0 3.76e+00 0.9 1.32e-02 8.30e-03h 1
47 1.7819511e+03 2.98e+00 2.33e+02 -1.0 3.78e+00 0.4 1.62e-02 2.00e-02h 1
48 1.7985805e+03 2.92e+00 2.72e+02 -1.0 3.56e+00 0.9 4.58e-02 1.96e-02h 1
49 1.8442748e+03 2.73e+00 2.59e+02 -1.0 3.54e+00 0.4 1.66e-02 6.39e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
50 1.8743367e+03 2.63e+00 2.76e+02 -1.0 3.31e+00 0.8 6.25e-02 3.91e-02h 1
51 1.9238778e+03 2.42e+00 2.57e+02 -1.0 3.27e+00 0.3 7.01e-02 8.00e-02f 1
52 1.9828630e+03 2.20e+00 2.10e+02 -1.0 3.02e+00 0.8 5.22e-02 8.74e-02h 1
53 2.0095513e+03 2.08e+00 1.93e+02 -1.0 2.77e+00 0.3 6.51e-02 5.52e-02f 1
54 2.0394719e+03 1.97e+00 2.04e+02 -1.0 2.65e+00 0.7 1.07e-01 5.27e-02h 1
55 2.0851337e+03 1.75e+00 1.53e+02 -1.0 2.48e+00 0.2 1.59e-01 1.11e-01f 1
56 2.1027078e+03 1.69e+00 1.49e+02 -1.0 2.43e+00 0.7 5.20e-02 3.71e-02h 1
57 2.1297528e+03 1.60e+00 8.57e+01 -1.0 2.34e+00 1.1 2.07e-02 5.28e-02h 1
58 2.1464470e+03 1.54e+00 7.32e+01 -1.0 2.23e+00 0.6 1.34e-01 3.91e-02h 1
59 2.1713332e+03 1.46e+00 4.88e+01 -1.0 2.16e+00 1.0 3.45e-02 5.24e-02h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
60 2.1868472e+03 1.40e+00 3.97e+01 -1.0 2.04e+00 0.6 2.53e-01 3.96e-02h 1
61 2.2027337e+03 1.35e+00 3.18e+01 -1.0 1.98e+00 1.0 2.53e-02 3.61e-02h 1
62 2.2721944e+03 1.08e+00 2.23e+01 -1.0 1.89e+00 0.5 1.81e-01 1.96e-01f 1
63 2.3057196e+03 9.75e-01 2.35e+02 -1.0 1.55e+00 0.9 3.46e-01 1.01e-01h 1
64 2.3301365e+03 8.70e-01 1.83e+02 -1.0 1.32e+00 0.5 1.73e-01 1.08e-01h 1
65 2.3426662e+03 8.28e-01 1.86e+02 -1.0 1.23e+00 0.9 8.38e-02 4.80e-02h 1
66 2.3862557e+03 6.14e-01 1.92e+02 -1.0 1.08e+00 0.4 1.33e-01 2.58e-01f 1
67 2.4189419e+03 4.99e-01 1.67e+02 -1.0 8.33e-01 0.8 4.15e-01 1.88e-01h 1
68 2.4508750e+03 4.02e-01 1.24e+02 -1.0 6.91e-01 1.3 1.85e-01 1.95e-01h 1
69 2.4941566e+03 2.23e-01 4.80e+01 -1.0 5.20e-01 0.8 5.48e-01 4.45e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
70 2.5170285e+03 1.43e-01 3.49e+02 -1.0 2.91e-01 1.2 9.42e-01 3.59e-01h 1
71 2.5153722e+03 4.85e-02 6.93e+01 -1.0 1.92e-01 0.7 5.18e-01 6.61e-01h 1
72 2.5138413e+03 2.45e-02 4.00e+01 -1.0 7.12e-02 1.2 4.71e-01 4.94e-01h 1
73 2.4921549e+03 1.43e-02 2.33e+01 -1.0 2.07e-01 0.7 4.16e-01 4.16e-01f 1
74 2.4809807e+03 5.55e-03 9.09e+02 -1.0 8.69e-02 1.1 8.93e-01 6.13e-01h 1
75 2.4477302e+03 2.71e-03 1.96e+02 -1.0 5.49e-01 0.6 4.02e-01 5.12e-01f 1
76 2.4368487e+03 1.43e-03 8.61e+02 -1.0 1.65e-01 1.0 1.56e-01 4.73e-01h 1
77 2.4051270e+03 7.99e-04 7.38e+02 -1.0 2.40e-01 0.6 7.97e-01 4.58e-01f 1
78 2.4014757e+03 6.83e-04 2.31e+03 -1.0 8.96e-02 1.0 1.00e+00 1.46e-01f 3
79 2.3518603e+03 1.20e-03 1.19e+03 -1.0 2.57e-01 0.5 1.00e+00 6.79e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
80 2.3255123e+03 3.64e-04 9.44e+00 -1.0 9.38e-02 0.9 1.00e+00 1.00e+00f 1
81 2.2740057e+03 1.85e-03 9.76e+02 -1.0 2.50e-01 0.5 1.00e+00 6.91e-01f 1
82 2.2490742e+03 4.66e-04 1.44e+01 -1.0 1.03e-01 0.9 1.00e+00 1.00e+00f 1
83 2.2209735e+03 9.21e-04 1.42e+03 -1.0 2.68e-01 0.4 1.00e+00 3.87e-01f 1
84 2.1973936e+03 6.00e-04 1.99e+02 -1.0 9.67e-02 0.8 1.00e+00 9.11e-01f 1
85 2.1523808e+03 2.39e-03 6.78e+02 -1.0 2.67e-01 0.4 1.00e+00 6.62e-01f 1
86 2.1362393e+03 1.08e-03 6.08e+02 -1.0 9.86e-02 0.8 1.00e+00 6.77e-01f 1
87 2.1059173e+03 3.17e-03 7.12e+02 -1.0 7.30e-01 0.3 8.14e-01 4.77e-01f 1
88 2.0834791e+03 5.72e-04 8.21e+01 -1.0 1.01e-01 0.7 1.00e+00 1.00e+00f 1
89 2.0279685e+03 4.02e-03 3.37e+02 -1.0 2.86e-01 0.3 6.68e-01 8.80e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
90 2.0066359e+03 6.99e-04 2.71e+00 -1.0 1.26e-01 0.7 1.00e+00 1.00e+00f 1
91 1.9821736e+03 1.33e-03 8.38e+02 -1.0 2.51e-01 0.2 1.00e+00 4.09e-01f 1
92 1.9608794e+03 8.55e-04 3.41e+00 -1.0 9.39e-02 0.6 1.00e+00 1.00e+00f 1
93 1.9261799e+03 2.55e-03 3.90e+02 -1.0 3.06e-01 0.2 8.66e-01 5.71e-01f 1
94 1.9050237e+03 1.03e-03 1.20e+01 -1.0 1.11e-01 0.6 1.00e+00 1.00e+00f 1
95 1.8590061e+03 6.53e-03 2.45e+02 -1.0 6.92e-01 0.1 5.61e-01 7.61e-01f 1
96 1.8566815e+03 2.69e-03 9.81e+02 -1.0 1.23e-01 1.4 3.18e-01 1.00e+00f 1
97 1.8532919e+03 1.53e-03 6.50e+02 -1.0 1.98e-01 1.0 1.00e+00 4.34e-01f 1
98 1.8300434e+03 1.50e-03 1.12e+02 -1.0 1.53e-01 0.5 1.00e+00 1.00e+00f 1
99 1.8218076e+03 2.25e-04 1.70e+02 -1.0 5.75e-02 0.9 8.45e-01 1.00e+00f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
100 1.7980477e+03 4.25e-03 7.14e+02 -1.0 3.55e-01 0.4 4.18e-01 1.00e+00f 1
101 1.7980588e+03 2.81e-03 6.92e+03 -1.0 8.48e-02 2.7 2.72e-01 1.00e+00h 1
102 1.7979721e+03 2.10e-03 5.34e+03 -1.0 1.94e-01 2.2 1.00e+00 2.41e-01h 1
103 1.7979089e+03 1.93e-03 5.05e+03 -1.0 2.37e+00 1.7 6.86e-01 5.13e-02f 2
104 1.7975030e+03 4.63e-04 9.45e+02 -1.0 1.20e-01 2.1 1.00e+00 1.00e+00h 1
105 1.7962014e+03 6.11e-05 1.10e+01 -1.0 8.56e-03 1.7 1.00e+00 1.00e+00f 1
106 1.7922792e+03 3.01e-04 5.26e+00 -1.0 8.06e-02 1.2 1.00e+00 1.00e+00f 1
107 1.7822273e+03 4.33e-04 9.64e+01 -1.0 6.45e-02 0.7 1.00e+00 8.95e-01f 1
108 1.7573063e+03 3.63e-03 1.37e+02 -1.0 1.85e-01 0.2 1.00e+00 8.47e-01f 1
109 1.7414203e+03 4.32e-03 4.61e+02 -1.0 8.14e-01 -0.2 7.06e-01 2.30e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
110 1.7225234e+03 4.11e-03 1.87e+02 -1.0 2.39e-01 0.2 1.00e+00 7.88e-01f 1
111 1.6945314e+03 9.93e-03 1.29e+02 -1.0 6.61e-01 -0.3 5.17e-01 4.72e-01f 1
112 1.6841097e+03 6.16e-03 3.21e+02 -1.0 2.49e-01 0.1 9.21e-01 5.59e-01f 1
113 1.6785266e+03 8.63e-04 3.79e-01 -1.0 9.44e-02 0.6 1.00e+00 1.00e+00f 1
114 1.6265266e+03 5.15e-04 1.34e+01 -2.5 1.66e-01 0.1 6.49e-01 4.10e-01f 1
115 1.5491916e+03 2.10e-03 1.08e+01 -2.5 5.00e-01 -0.4 4.64e-01 4.25e-01f 1
116 1.5119139e+03 1.45e-03 7.07e+00 -2.5 1.95e-01 0.0 5.04e-01 4.57e-01f 1
117 1.5006965e+03 1.02e-03 2.74e+01 -2.5 7.46e-02 0.5 8.12e-01 3.13e-01f 1
118 1.4762919e+03 8.72e-04 3.20e+01 -2.5 2.18e-01 -0.0 8.97e-01 3.41e-01f 1
119 1.4468469e+03 2.61e-04 8.77e-01 -2.5 8.37e-02 0.4 1.00e+00 9.90e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
120 1.4300874e+03 3.32e-04 3.86e+01 -2.5 2.41e-01 -0.1 1.00e+00 2.63e-01f 1
121 1.4165327e+03 4.18e-04 4.12e+01 -2.5 6.62e-01 -0.6 5.38e-01 8.83e-02f 1
122 1.3956178e+03 6.43e-04 3.13e+01 -2.5 2.63e-01 -0.1 8.12e-01 3.59e-01f 1
123 1.3737474e+03 1.23e-03 3.34e+01 -2.5 7.06e-01 -0.6 5.43e-01 1.75e-01f 1
124 1.3551125e+03 1.41e-03 2.73e+01 -2.5 2.69e-01 -0.2 8.32e-01 4.15e-01f 1
125 1.3498510e+03 1.01e-03 3.47e+01 -2.5 9.26e-02 0.2 1.00e+00 3.35e-01f 1
126 1.3418493e+03 1.03e-03 3.47e+01 -2.5 2.48e-01 -0.2 7.11e-01 2.38e-01f 1
127 1.3196772e+03 2.70e-03 2.64e+01 -2.5 6.66e-01 -0.7 3.39e-01 2.72e-01f 1
128 1.3158288e+03 2.72e-03 2.98e+01 -2.5 1.84e+00 -1.2 1.60e-01 1.89e-02f 1
129 1.3025329e+03 3.05e-03 2.50e+01 -2.5 6.96e-01 -0.8 1.90e-01 1.76e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
130 1.2965755e+03 2.95e-03 2.63e+01 -2.5 4.34e+00 -1.2 1.14e-01 3.03e-02f 1
131 1.2866777e+03 2.57e-03 2.09e+01 -2.5 8.25e-01 -0.8 4.58e-02 1.27e-01f 1
132 1.2777333e+03 2.15e-03 2.25e+01 -2.5 4.05e-01 -0.4 5.41e-01 2.92e-01f 1
133 1.2711780e+03 1.80e-03 2.25e+01 -2.5 2.34e-01 0.0 1.00e+00 5.69e-01f 1
134 1.2689198e+03 1.93e-03 3.35e+01 -2.5 8.00e-01 -0.4 5.10e-01 7.77e-02f 1
135 1.2676457e+03 1.76e-04 1.21e+01 -2.5 1.56e-02 0.9 9.51e-01 9.07e-01f 1
136 1.2676473e+03 3.87e-05 8.42e+01 -2.5 1.79e-03 4.0 1.00e+00 1.00e+00h 1
137 1.2676474e+03 1.54e-05 1.50e+02 -2.5 2.96e-03 4.5 5.18e-01 1.00e+00f 1
138 1.2676448e+03 1.56e-03 1.05e+04 -2.5 3.47e-02 4.0 1.00e+00 1.00e+00f 1
139 1.2676390e+03 3.20e-04 2.30e+03 -2.5 2.10e-02 3.5 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
140 1.2676265e+03 3.50e-05 6.11e+02 -2.5 1.02e-02 3.0 1.00e+00 1.00e+00h 1
141 1.2675925e+03 2.36e-05 1.59e+02 -2.5 4.31e-03 2.5 1.00e+00 1.00e+00f 1
142 1.2674941e+03 3.14e-05 2.62e+01 -2.5 1.07e-03 2.1 1.00e+00 1.00e+00f 1
143 1.2672142e+03 8.56e-06 2.96e+01 -2.5 3.01e-03 1.6 1.00e+00 1.00e+00f 1
144 1.2664294e+03 8.89e-06 8.40e+00 -2.5 9.11e-03 1.1 1.00e+00 1.00e+00f 1
145 1.2642678e+03 5.21e-05 4.07e-01 -2.5 2.70e-02 0.6 1.00e+00 1.00e+00f 1
146 1.2581090e+03 3.73e-04 1.17e-01 -2.5 7.99e-02 0.2 1.00e+00 1.00e+00f 1
147 1.2536180e+03 3.81e-04 3.82e+01 -2.5 2.36e-01 -0.3 1.00e+00 2.56e-01f 1
148 1.2477186e+03 3.94e-04 3.52e+01 -2.5 6.78e-01 -0.8 2.58e-01 1.24e-01f 1
149 1.2399618e+03 7.15e-04 3.31e+01 -2.5 1.85e+00 -1.3 9.34e-02 7.15e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
150 1.2391203e+03 6.10e-04 3.01e+01 -2.5 8.84e-02 0.1 2.77e-01 1.56e-01f 1
151 1.2365711e+03 5.73e-04 2.52e+01 -2.5 2.45e-01 -0.4 1.76e-01 1.68e-01f 1
152 1.2302605e+03 1.83e-03 2.18e+01 -2.5 8.94e-01 -0.9 1.61e-01 1.48e-01f 1
153 1.2224414e+03 2.69e-03 2.13e+01 -2.5 1.99e+00 -1.4 1.09e-01 7.34e-02f 1
154 1.2191867e+03 2.76e-03 2.50e+01 -2.5 7.36e-01 -0.9 2.61e-01 7.97e-02f 1
155 1.2106580e+03 3.70e-03 2.25e+01 -2.5 2.45e+00 -1.4 6.81e-02 8.44e-02f 1
156 1.2083245e+03 3.63e-03 2.39e+01 -2.5 8.42e-01 -1.0 1.63e-01 6.55e-02f 1
157 1.2035856e+03 3.94e-03 2.34e+01 -2.5 3.46e+00 -1.5 9.05e-02 5.64e-02f 1
158 1.1991227e+03 4.57e-03 2.55e+01 -2.5 1.17e+00 -1.0 3.15e-01 1.32e-01f 1
159 1.1933142e+03 7.42e-03 2.34e+01 -2.5 4.40e+00 -1.5 7.19e-02 7.65e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
160 1.1919710e+03 7.26e-03 2.36e+01 -2.5 1.46e+00 -1.1 9.56e-02 4.90e-02f 1
161 1.1839303e+03 1.18e-02 2.04e+01 -2.5 3.20e+00 -1.6 1.04e-01 1.18e-01f 1
162 1.1815940e+03 1.12e-02 1.89e+01 -2.5 1.21e+00 -1.2 1.05e-01 9.26e-02f 1
163 1.1806864e+03 1.11e-02 2.06e+01 -2.5 3.24e+00 -1.6 7.47e-02 1.60e-02f 1
164 1.1769223e+03 1.12e-02 1.26e+01 -2.5 1.31e+00 -1.2 2.53e-02 1.75e-01f 1
165 1.1736637e+03 1.20e-02 1.48e+01 -2.5 3.21e+00 -1.7 1.39e-01 5.97e-02f 1
166 1.1727945e+03 1.18e-02 1.72e+01 -2.5 1.15e+01 -2.2 7.80e-02 9.72e-03f 1
167 1.1686713e+03 1.08e-02 1.62e+01 -2.5 3.32e+00 -1.7 1.29e-01 1.07e-01f 1
168 1.1679248e+03 1.03e-02 1.49e+01 -2.5 8.87e-01 -1.3 2.77e-02 4.43e-02f 1
169 1.1663288e+03 9.78e-03 1.43e+01 -2.5 2.28e+00 -1.8 5.39e-02 4.89e-02f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
170 1.1652814e+03 8.97e-03 1.94e+01 -2.5 8.56e-01 -1.4 2.50e-01 8.33e-02f 1
171 1.1642213e+03 6.97e-03 2.06e+01 -2.5 3.07e-01 -0.9 3.93e-01 2.22e-01f 1
172 1.1609728e+03 5.00e-03 1.30e+01 -2.5 9.49e-01 -1.4 2.25e-01 2.83e-01f 1
173 1.1574103e+03 4.71e-03 1.09e+01 -2.5 2.80e+00 -1.9 1.21e-01 1.32e-01f 1
174 1.1540011e+03 5.18e-03 9.23e+00 -2.5 1.04e+00 -1.5 3.35e-01 2.96e-01f 1
175 1.1523907e+03 3.43e-03 1.55e+01 -2.5 3.35e-01 -1.0 6.51e-01 4.16e-01f 1
176 1.1504710e+03 3.52e-03 1.99e+01 -2.5 9.50e-01 -1.5 4.22e-01 2.12e-01f 1
177 1.1475558e+03 2.48e-03 6.14e+00 -2.5 3.61e-01 -1.1 9.62e-01 8.59e-01f 1
178 1.1430276e+03 8.92e-03 9.87e+00 -2.5 1.10e+00 -1.6 7.28e-01 5.68e-01f 1
179 1.1428439e+03 1.68e-04 2.47e+01 -2.5 7.48e-02 -0.2 4.02e-01 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
180 1.1418173e+03 4.53e-04 2.23e+00 -2.5 1.48e-01 -0.7 9.71e-01 1.00e+00f 1
181 1.1391057e+03 3.93e-03 2.41e+00 -2.5 4.35e-01 -1.2 1.00e+00 1.00e+00f 1
182 1.1367858e+03 6.48e-03 2.89e+00 -2.5 1.17e+00 -1.7 4.03e-01 3.75e-01f 1
183 1.1355444e+03 3.97e-03 7.93e+00 -2.5 4.15e-01 -1.2 4.01e-01 5.74e-01f 1
184 1.1338700e+03 5.83e-03 3.43e+01 -2.5 1.18e+00 -1.7 1.00e+00 3.26e-01f 1
185 1.1320604e+03 3.89e-03 2.14e-01 -2.5 4.25e-01 -1.3 1.00e+00 1.00e+00f 1
186 1.1306842e+03 5.24e-03 1.45e+01 -2.5 1.01e+00 -1.8 6.69e-01 3.83e-01f 1
187 1.1296041e+03 3.13e-03 9.93e+00 -2.5 4.00e-01 -1.3 1.00e+00 8.71e-01f 1
188 1.1292183e+03 4.64e-04 1.99e+00 -2.5 1.51e-01 -0.9 1.00e+00 1.00e+00h 1
189 1.1282366e+03 2.74e-03 4.28e+00 -2.5 4.29e-01 -1.4 1.00e+00 9.16e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
190 1.1266451e+03 1.25e-02 8.10e+00 -2.5 1.19e+00 -1.9 4.95e-01 6.98e-01f 1
191 1.1260389e+03 1.36e-02 4.19e+01 -2.5 2.92e+00 -2.3 9.81e-01 1.49e-01h 1
192 1.1244310e+03 5.19e-02 6.62e+00 -2.5 1.26e+00 -1.9 4.24e-01 1.00e+00h 1
193 1.1244881e+03 3.37e-02 2.20e+03 -2.5 1.03e+00 0.3 1.37e-01 7.38e-01h 1
194 1.1245189e+03 3.81e-03 5.34e+02 -2.5 2.70e-01 0.7 1.00e+00 1.00e+00h 1
195 1.1245068e+03 1.17e-03 8.73e+01 -2.5 1.89e-01 0.3 1.00e+00 1.00e+00h 1
196 1.1244683e+03 2.33e-05 2.30e+00 -2.5 3.20e-02 -0.2 1.00e+00 1.00e+00h 1
197 1.1243552e+03 1.54e-04 1.71e-02 -2.5 8.42e-02 -0.7 1.00e+00 1.00e+00f 1
198 1.1190994e+03 6.09e-04 1.51e+00 -3.8 2.82e-01 -1.2 5.92e-01 6.86e-01f 1
199 1.1180288e+03 8.34e-04 2.92e+00 -3.8 6.39e-01 -1.6 4.57e-01 2.24e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
200 1.1159998e+03 7.95e-03 4.85e+00 -3.8 1.57e+00 -2.1 5.44e-01 3.25e-01f 1
201 1.1147116e+03 6.52e-03 6.39e+00 -3.8 6.37e-01 -1.7 7.88e-01 4.54e-01f 1
202 1.1141096e+03 3.62e-03 2.20e+00 -3.8 2.46e-01 -1.3 1.18e-01 5.01e-01h 1
203 1.1139708e+03 3.40e-03 3.80e+00 -3.8 6.49e-01 -1.7 3.48e-01 9.09e-02h 1
204 1.1136362e+03 2.51e-05 6.03e-01 -3.8 3.60e-02 -0.4 1.00e+00 1.00e+00h 1
205 1.1133723e+03 2.70e-04 2.79e-02 -3.8 1.02e-01 -0.9 1.00e+00 1.00e+00f 1
206 1.1133151e+03 3.71e-05 3.43e-02 -3.8 3.74e-02 -0.5 1.00e+00 1.00e+00h 1
207 1.1131350e+03 3.29e-04 2.78e-01 -3.8 1.09e-01 -0.9 1.00e+00 1.00e+00f 1
208 1.1127639e+03 1.69e-03 5.67e+00 -3.8 3.05e-01 -1.4 4.09e-01 7.62e-01f 1
209 1.1124053e+03 3.18e-03 1.36e+00 -3.8 8.06e-01 -1.9 5.54e-01 3.11e-01f 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
210 1.1118494e+03 8.48e-03 5.05e+00 -3.8 1.95e+00 -2.4 4.87e-01 2.16e-01f 1
211 1.1114165e+03 1.22e-02 4.92e+00 -3.8 4.02e+00 -2.9 1.21e-01 9.06e-02f 1
212 1.1111748e+03 1.31e-02 5.94e+00 -3.8 8.10e+00 -3.3 1.38e-01 3.23e-02f 1
213 1.1109347e+03 1.32e-02 7.87e+00 -3.8 6.67e+00 -2.9 2.79e-01 5.54e-02h 1
214 1.1104649e+03 1.65e-02 7.34e+00 -3.8 7.56e+00 -3.4 9.00e-02 7.91e-02f 1
215 1.1103271e+03 1.65e-02 1.07e+01 -3.8 4.06e+00 -3.0 4.62e-01 4.32e-02h 1
216 1.1098444e+03 2.77e-02 9.93e+00 -3.8 7.43e+00 -3.4 1.62e-01 1.01e-01h 1
217 1.1098538e+03 1.90e-02 1.18e+01 -3.8 5.39e-02 -0.3 3.23e-01 3.16e-01h 1
218 1.1098809e+03 1.10e-05 5.82e+00 -3.8 1.11e-02 0.1 1.00e+00 1.00e+00h 1
219 1.1098622e+03 1.08e-05 1.06e+00 -3.8 1.90e-02 -0.4 1.00e+00 1.00e+00h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
220 1.1098107e+03 5.25e-05 2.18e-01 -3.8 5.49e-02 -0.8 1.00e+00 1.00e+00h 1
221 1.1096817e+03 4.04e-04 1.06e+00 -3.8 1.64e-01 -1.3 1.00e+00 9.34e-01h 1
222 1.1095749e+03 6.50e-04 1.10e+01 -3.8 4.73e-01 -1.8 1.00e+00 3.17e-01f 1
223 1.1095621e+03 8.31e-06 1.21e+00 -3.8 2.29e-02 -0.5 7.63e-01 1.00e+00h 1
224 1.1095140e+03 7.70e-05 1.21e-01 -3.8 6.81e-02 -0.9 1.00e+00 1.00e+00h 1
225 1.1093825e+03 6.62e-04 1.60e-01 -3.8 2.01e-01 -1.4 1.00e+00 1.00e+00h 1
226 1.1093364e+03 6.74e-04 1.37e+01 -3.8 5.66e-01 -1.9 1.00e+00 1.44e-01h 1
227 1.1092690e+03 5.38e-04 7.05e+00 -3.8 2.20e-01 -1.5 1.00e+00 5.60e-01h 1
228 1.1090343e+03 3.55e-03 5.58e-01 -3.8 6.20e-01 -1.9 5.37e-01 7.49e-01f 1
229 1.1087697e+03 8.51e-03 3.15e+00 -3.8 1.59e+00 -2.4 6.12e-01 4.12e-01h 1
iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls
230 1.1087608e+03 3.38e-03 6.31e+00 -3.8 8.48e-02 -1.1 1.00e+00 6.07e-01h 1
231 1.1087556e+03 1.19e-05 3.16e-01 -3.8 3.19e-02 -0.7 1.00e+00 1.00e+00h 1
232 1.1087186e+03 1.25e-04 1.24e-02 -3.8 9.27e-02 -1.1 1.00e+00 1.00e+00h 1
Number of Iterations....: 232
(scaled) (unscaled)
Objective...............: 1.1087186343198964e+03 1.1087186343198964e+03
Dual infeasibility......: 1.2357098800516109e-02 1.2357098800516109e-02
Constraint violation....: 1.2474641167337097e-04 1.2474641167337097e-04
Variable bound violation: 6.5439683696740520e-09 6.5439683696740520e-09
Complementarity.........: 1.5237086683517976e-04 1.5237086683517976e-04
Overall NLP error.......: 5.0040582267332004e-03 1.2357098800516109e-02
Number of objective function evaluations = 238
Number of objective gradient evaluations = 233
Number of equality constraint evaluations = 238
Number of inequality constraint evaluations = 239
Number of equality constraint Jacobian evaluations = 233
Number of inequality constraint Jacobian evaluations = 233
Number of Lagrangian Hessian evaluations = 232
Total seconds in IPOPT (w/o function evaluations) = 61.769
Total seconds in NLP function evaluations = 69.785
Timing Statistics:
OverallAlgorithm....................: 131.553 (sys: 0.000 wall: 131.553)
PrintProblemStatistics.............: 0.001 (sys: 0.000 wall: 0.001)
InitializeIterates.................: 0.140 (sys: 0.000 wall: 0.140)
UpdateHessian......................: 41.388 (sys: 0.000 wall: 41.388)
OutputIteration....................: 0.348 (sys: 0.000 wall: 0.348)
UpdateBarrierParameter.............: 0.155 (sys: 0.000 wall: 0.155)
ComputeSearchDirection.............: 57.473 (sys: 0.000 wall: 57.474)
ComputeAcceptableTrialPoint........: 23.227 (sys: 0.000 wall: 23.227)
AcceptTrialPoint...................: 0.155 (sys: 0.000 wall: 0.155)
CheckConvergence...................: 8.666 (sys: 0.000 wall: 8.666)
PDSystemSolverTotal.................: 57.125 (sys: 0.000 wall: 57.125)
PDSystemSolverSolveOnce............: 53.360 (sys: 0.000 wall: 53.361)
ComputeResiduals...................: 3.091 (sys: 0.000 wall: 3.091)
StdAugSystemSolverMultiSolve.......: 52.663 (sys: 0.000 wall: 52.664)
LinearSystemScaling................: 0.000 (sys: 0.000 wall: 0.000)
LinearSystemSymbolicFactorization..: 0.129 (sys: 0.000 wall: 0.129)
LinearSystemFactorization..........: 44.336 (sys: 0.000 wall: 44.336)
LinearSystemBackSolve..............: 5.916 (sys: 0.000 wall: 5.918)
LinearSystemStructureConverter.....: 0.000 (sys: 0.000 wall: 0.000)
LinearSystemStructureConverterInit: 0.000 (sys: 0.000 wall: 0.000)
QualityFunctionSearch...............: 0.000 (sys: 0.000 wall: 0.000)
TryCorrector........................: 0.000 (sys: 0.000 wall: 0.000)
Task1...............................: 0.000 (sys: 0.000 wall: 0.000)
Task2...............................: 0.000 (sys: 0.000 wall: 0.000)
Task3...............................: 0.000 (sys: 0.000 wall: 0.000)
Task4...............................: 0.000 (sys: 0.000 wall: 0.000)
Task5...............................: 0.000 (sys: 0.000 wall: 0.000)
Task6...............................: 0.000 (sys: 0.000 wall: 0.000)
Function Evaluations................: 69.785 (sys: 0.000 wall: 69.785)
Objective function.................: 0.010 (sys: 0.000 wall: 0.010)
Objective function gradient........: 0.096 (sys: 0.000 wall: 0.096)
Equality constraints...............: 21.362 (sys: 0.000 wall: 21.362)
Inequality constraints.............: 0.029 (sys: 0.000 wall: 0.029)
Equality constraint Jacobian.......: 0.172 (sys: 0.000 wall: 0.172)
Inequality constraint Jacobian.....: 6.962 (sys: 0.000 wall: 6.962)
Lagrangian Hessian.................: 41.154 (sys: 0.000 wall: 41.154)
EXIT: Optimal Solution Found.
```
---
### Author:  [@odow](https://discourse.julialang.org/u/odow)
#### Post date: [January 30, 2024, 8:07pm UTC](https://discourse.julialang.org/t/long-nlp-evaluation-time-in-ipopt/109436/2 "2024-01-30T20:07:30Z")
Hi @tso-martin, welcome to the forum.
Can you provide a reproducible example? What happens if you use a different linear solver?
Is something special about the equality constraints?
---
### Author:  [@cvanaret](https://discourse.julialang.org/u/cvanaret)
#### Post date: [January 30, 2024, 9:00pm UTC](https://discourse.julialang.org/t/long-nlp-evaluation-time-in-ipopt/109436/3 "2024-01-30T21:00:08Z")
Is there any chance you can provide a good starting point that satisfies most (or all) of the constraints?
---
### Author:  [@ccoffrin](https://discourse.julialang.org/u/ccoffrin)
#### Post date: [January 31, 2024, 4:22am UTC](https://discourse.julialang.org/t/long-nlp-evaluation-time-in-ipopt/109436/4 "2024-01-31T04:22:26Z")
> [@tso-martin](#):
>
> Are there any suggestions or indications on how to improve the performance of the solving process? Your help is highly appreciated.
From a quick glance at the Ipopt log, the number of iterations to convergence seems high (but not clearly unreasonable). I would say around 50-100 is more typical (in my experience) for a well posed AC OPF type of problem.
Given that you said you are doing SCOPF, my first thought is do you have a lot of equality constraints of the form `x_{first stage} == x_{contingency stage}` in the model? This can slow down Ipopt’s convergence a lot because it does not have a pre-solver to eliminate variables. You would want to do the variable replacement in your optimization modeling layer.
Another thought is the quality of the network data you are using. Very small or very large values on any of the power components (e.g., shunts, branches) can be problematic. I would do some data analysis on your network model to see if there any parameters can the be cleaned up.
---
### Author:  [@tso-martin](https://discourse.julialang.org/u/tso-martin)
#### Post date: [January 31, 2024, 2:25pm UTC](https://discourse.julialang.org/t/long-nlp-evaluation-time-in-ipopt/109436/5 "2024-01-31T14:25:33Z")
Thank you for the first hints. You can checkout the “minimal” working example in [https://github.com/tso-martin/example\_scopf.git](https://github.com/tso-martin/example_scopf.git). The problem itself is a multiperiod SCOPF for an adapted case39 network modelled with PowerModels (ACPPowerModel).
The equality constraints are special in way, that they contain non-linear sine and cosine terms (`constraint_ohms_y_pst_from`).
```julia
JuMP.@NLconstraint(pm.model, p_fr == (g+g_fr)/tm^2*vm_fr^2 + (-g)/tm*(vm_fr*vm_to*cos(va_fr-va_to-ta)) + (-b)/tm*(vm_fr*vm_to*sin(va_fr-va_to-ta)) )
JuMP.@NLconstraint(pm.model, q_fr == -(b+b_fr)/tm^2*vm_fr^2 - (-b)/tm*(vm_fr*vm_to*cos(va_fr-va_to-ta)) + (-g)/tm*(vm_fr*vm_to*sin(va_fr-va_to-ta)) )
```
I checked with linear solvers MUMPS, MA57 and MA97. They all require more than 150 iterations.
I warm-start the primal values by using single-period OPF results.
Concerning the equality constraints, I will have a look into that.
---
### Author:  [@ccoffrin](https://discourse.julialang.org/u/ccoffrin)
#### Post date: [February 1, 2024, 2:54am UTC](https://discourse.julialang.org/t/long-nlp-evaluation-time-in-ipopt/109436/6 "2024-02-01T02:54:24Z")
> [@tso-martin](#):
>
> I warm-start the primal values by using single-period OPF results.
I would recommend a flat start instead (i.e., vm = 1; va, pg, qg = 0.0). This tends to have the best behavior in AC-OPF with Ipopt.
---
### Author:  [@tso-martin](https://discourse.julialang.org/u/tso-martin)
#### Post date: [February 14, 2024, 6:56am UTC](https://discourse.julialang.org/t/long-nlp-evaluation-time-in-ipopt/109436/7 "2024-02-14T06:56:32Z")
Thanks again for your help. I tested the flat start and got slight performance improvements.