[Ipopt] Restoration Phase and Scaling
Stefan Vigerske
stefan at math.hu-berlin.de
Mon Jul 25 09:22:28 EDT 2016
Hi,
yes, the restoration phase is about reducing constraint violation only,
that is, trying to find a minimal infeasible point.
It is described in Section 3.3 of the Ipopt implementation paper
http://www.optimization-online.org/DB_HTML/2004/03/836.html
If you increase the print_level of Ipopt, you may also get some more
information on why Ipopt entered the restoration phase, i.e., whether
the step size became too small (A-5.10 in Section 2.5) or the linear
system seems too illconditioned (IC-6 in Section 3.1).
Hope that helps,
Stefan
On 07/19/2016 08:55 PM, Johannes Maußner wrote:
> Hi everyone,
>
> I'm quite new to using IPOPT and optimization in general so I'm sorry in
> advance if this question is trivial.
> I'm working on an optimization problem that is constrained by a system
> of coupled partial differential equations
> (conservation equations) and I'm using IPOPT through AMPL.
>
> I set up two "versions" of the model. The first one is not scaled and
> for the second one I introduced reference values
> to my model to scale the state and decision variables. This scaling is
> done inside AMPL before the problem is send to the solver.
>
> Both models eventually converge to a feasible point and yield the same
> results. However the scaled model converges faster
> and without entering the "restoration phase" whereas the model which is
> not scaled usually enters the restoration phase at some
> point (example below).
> My question is what exactly happens during the "restoration phase" and what
> triggers this restoration phase? As far as I understand it, during this
> phase IPOPT tries to minimize the infeasiblity. Is this correct?
>
> Below is the solver log for an optimization using the unscaled model. Up
> to the 10th iteration it looks quite good and the
> objective is near the optimal point but then it gets into the
> restoration phase. It takes about 100 iterations before the solver exits
> this phase and
> then converges to the optimal point.
> I don't quite understand why this restoration phase happens.
>
> I'll be using the scaled model anyway but I'm just curious as to why
> this restoration phase happens and what it means exactly.
> I'm very grateful for any help!
>
> Thanks a lot,
> Johannes
>
>
> ******************************************************************************
>
> 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
> ******************************************************************************
>
>
> This is Ipopt version 3.11, running with linear solver ma97.
>
> Number of nonzeros in equality constraint Jacobian...: 4603085
> Number of nonzeros in inequality constraint Jacobian.: 0
> Number of nonzeros in Lagrangian Hessian.............: 1597612
>
> Total number of variables............................: 107603
> variables with only lower bounds: 0
> variables with lower and upper bounds: 107603
> variables with only upper bounds: 0
> Total number of equality constraints.................: 107602
> 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
>
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
> alpha_pr ls
> 0 -5.0000000e-01 4.11e-01 2.63e-03 -1.0 0.00e+00 - 0.00e+00
> 0.00e+00 0
> 1 -4.3846879e-01 9.64e+00 5.37e+05 -1.0 4.02e+04 - 1.21e-01
> 4.82e-01f 1
> 2 -4.6909814e-01 1.69e+01 9.73e+05 -1.0 2.46e+06 - 2.47e-01
> 6.28e-02h 1
> 3 -7.5397593e-01 1.44e+01 2.03e+07 -1.0 3.07e+04 - 3.16e-04
> 8.36e-01h 1
> 4 -8.1497281e-01 1.11e+01 1.08e+07 -1.0 1.69e+02 - 5.58e-01
> 7.76e-01f 1
> 5 -8.2927768e-01 1.35e+00 5.55e+07 -1.0 7.61e+01 - 1.89e-02
> 1.00e+00h 1
> 6 -8.2850533e-01 6.57e-01 1.02e+07 -1.0 4.61e+01 - 9.73e-01
> 1.00e+00h 1
> 7 -8.2842382e-01 3.97e-04 5.32e+04 -1.0 2.72e+00 - 9.74e-01
> 1.00e+00h 1
> 8 -8.2842114e-01 4.50e-06 6.24e+00 -1.0 1.48e+02 - 5.49e-01
> 1.00e+00f 1
> 9 -8.2798948e-01 4.06e+00 8.42e+01 -1.0 2.70e+04 - 1.20e-02
> 1.00e+00f 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
> alpha_pr ls
> 10 -8.2798511e-01 3.58e-05 2.41e-02 -1.0 3.89e+01 -4.0 1.00e+00
> 1.00e+00h 1
> 11r-8.2798511e-01 3.58e-05 1.00e+03 -2.5 0.00e+00 -1.8 0.00e+00
> 3.29e-07R 20
> 12r-8.2427337e-01 2.02e-02 1.45e+01 -2.5 3.35e+01 - 9.86e-01
> 1.00e+00f 1
> 13r-8.4615859e-01 5.21e-01 9.48e+02 -2.5 1.45e+02 - 8.05e-02
> 2.17e-01f 1
> 14r-9.3201299e-01 4.07e+00 9.60e+02 -2.5 9.10e+01 - 3.58e-01
> 7.73e-01f 1
> 15r-9.9932014e-01 2.43e+00 6.60e+02 -2.5 4.79e+02 - 1.74e-01
> 4.41e-01f 1
> 16r-9.9999321e-01 2.41e+00 6.20e+02 -2.5 4.12e+02 - 2.83e-01
> 9.03e-03f 1
> 17r-9.9903424e-01 1.93e+00 7.56e+02 -2.5 5.54e+02 - 4.29e-02
> 7.48e-01f 1
> 18r-9.9999035e-01 1.85e+00 6.12e+02 -2.5 8.06e+02 - 1.03e-01
> 6.82e-02f 1
> 19r-9.9995604e-01 2.94e+00 9.92e+02 -2.5 2.01e+03 - 2.71e-02
> 1.19e-01f 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
> alpha_pr ls
> 20r-9.9995125e-01 3.65e+00 1.05e+03 -2.5 1.46e+03 - 9.20e-02
> 1.61e-01f 1
> 21r-9.9994689e-01 3.53e+00 1.03e+03 -2.5 9.84e+02 - 1.72e-02
> 4.85e-02f 1
> 22r-9.9990940e-01 2.93e+00 7.50e+02 -2.5 4.66e+02 - 1.32e-01
> 3.46e-01f 1
> 23r-9.9990066e-01 2.53e+00 6.44e+02 -2.5 1.93e+01 - 2.45e-01
> 1.36e-01f 1
> 24r-9.9989093e-01 1.90e+00 4.81e+02 -2.5 7.07e+01 - 2.78e-01
> 2.53e-01f 1
> 25r-9.9989589e-01 1.50e+00 3.74e+02 -2.5 2.01e+02 - 2.88e-01
> 2.22e-01f 1
> 26r-9.9991351e-01 1.20e+00 2.93e+02 -2.5 2.75e+02 - 2.09e-01
> 2.17e-01f 1
> 27r-9.9992750e-01 9.07e-01 2.19e+02 -2.5 1.59e+02 - 2.52e-01
> 2.51e-01f 1
> 28r-9.9993996e-01 5.20e-01 1.27e+02 -2.5 1.09e+02 - 6.11e-01
> 4.28e-01f 1
> 29r-9.9994310e-01 3.53e-01 1.08e+02 -2.5 8.72e+01 - 1.00e+00
> 3.22e-01f 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
> alpha_pr ls
> 30r-9.9994871e-01 8.54e-02 5.93e-01 -2.5 6.66e+01 - 1.00e+00
> 1.00e+00f 1
> 31r-9.9994896e-01 8.62e-02 8.31e-03 -2.5 7.03e+00 - 1.00e+00
> 1.00e+00h 1
> 32r-9.9994500e-01 9.46e-02 4.33e+01 -3.8 7.14e+02 - 1.53e-01
> 1.99e-01f 1
> 33r-9.9994274e-01 9.96e-02 8.49e+01 -3.8 6.37e+00 -4.0 3.91e-02
> 1.19e-01f 1
> 34r-9.9993803e-01 1.04e-01 7.44e+01 -3.8 8.17e+00 -4.5 1.46e-01
> 1.49e-01f 1
> 35r-9.9993331e-01 1.08e-01 7.80e+01 -3.8 1.30e+01 -5.0 6.43e-02
> 8.38e-02f 1
> 36r-9.9992902e-01 1.09e-01 7.38e+01 -3.8 5.61e+02 - 5.24e-02
> 5.97e-02f 1
> 37r-9.9992510e-01 1.12e-01 7.34e+01 -3.8 2.91e+01 -5.4 4.37e-02
> 4.84e-02f 1
> 38r-9.9992222e-01 1.15e-01 7.19e+01 -3.8 2.34e+01 -5.0 4.73e-02
> 5.09e-02f 1
> 39r-9.9992017e-01 1.17e-01 6.98e+01 -3.8 1.79e+02 -5.5 2.08e-02
> 1.99e-02f 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
> alpha_pr ls
> 40r-9.9991818e-01 1.19e-01 6.22e+01 -3.8 3.36e+01 -5.1 4.60e-02
> 3.82e-02f 1
> 41r-9.9991883e-01 1.21e-01 5.75e+01 -3.8 2.73e+01 -4.6 5.58e-02
> 5.03e-02f 1
> 42r-9.9991870e-01 1.21e-01 9.91e+01 -3.8 2.69e+02 -5.1 7.33e-03
> 1.18e-03f 1
> 43r-9.9992016e-01 1.21e-01 9.72e+01 -3.8 3.35e+01 -4.7 4.93e-02
> 2.71e-02f 1
> 44r-9.9992081e-01 1.18e-01 9.79e+01 -3.8 8.44e+01 -5.2 1.99e-02
> 1.87e-02f 1
> 45r-9.9992199e-01 2.05e-01 9.23e+01 -3.8 5.94e+01 -4.7 4.23e-02
> 4.52e-02f 1
> 46r-9.9992105e-01 2.41e-01 8.50e+01 -3.8 7.10e+01 -4.3 1.11e-02
> 2.66e-02f 1
> 47r-9.9992147e-01 2.42e-01 8.73e+01 -3.8 5.32e+01 -3.9 3.42e-02
> 1.06e-02f 1
> 48r-9.9992499e-01 2.36e-01 1.46e+02 -3.8 1.51e+01 -3.5 1.71e-01
> 5.89e-02f 1
> 49r-9.9992585e-01 2.39e-01 2.31e+02 -3.8 6.04e+01 -3.9 4.22e-02
> 1.29e-02f 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
> alpha_pr ls
> 50r-9.9993494e-01 2.58e-01 1.60e+02 -3.8 1.56e+01 -3.5 1.05e-01
> 1.52e-01f 1
> 51r-9.9993546e-01 3.19e-01 1.07e+02 -3.8 4.39e+02 -4.0 2.75e-03
> 5.88e-03f 1
> 52r-9.9993813e-01 3.75e-01 1.06e+02 -3.8 5.83e+01 -3.6 5.25e-02
> 5.02e-02f 1
> 53r-9.9993971e-01 3.66e-01 3.31e+02 -3.8 2.05e+01 -3.1 2.47e-01
> 3.31e-02f 1
> 54r-9.9994004e-01 3.73e-01 5.10e+02 -3.8 1.79e+02 -3.6 2.99e-02
> 6.07e-03f 1
> 55r-9.9994232e-01 3.60e-01 5.55e+02 -3.8 1.77e+01 -3.2 1.61e-01
> 4.92e-02f 1
> 56r-9.9994296e-01 3.85e-01 5.56e+02 -3.8 1.54e+02 -3.7 1.60e-02
> 1.32e-02f 1
> 57r-9.9994512e-01 3.75e-01 5.22e+02 -3.8 2.37e+01 -3.2 2.92e-02
> 4.95e-02f 1
> 58r-9.9994505e-01 3.75e-01 5.35e+02 -3.8 4.31e+02 -3.7 7.38e-03
> 4.67e-04f 1
> 59r-9.9994680e-01 3.65e-01 4.92e+02 -3.8 2.19e+01 -3.3 7.98e-02
> 7.96e-02f 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
> alpha_pr ls
> 60r-9.9994616e-01 3.71e-01 4.88e+02 -3.8 5.17e+02 -3.8 4.36e-03
> 1.84e-03f 1
> 61r-9.9994614e-01 3.67e-01 5.53e+02 -3.8 2.46e+01 -3.3 1.20e-01
> 9.54e-03f 1
> 62r-9.9994338e-01 3.76e-01 6.00e+02 -3.8 1.09e+02 -3.8 2.50e-02
> 1.34e-02f 1
> 63r-9.9994131e-01 3.62e-01 6.55e+02 -3.8 2.08e+01 -3.4 1.85e-01
> 6.57e-02f 1
> 64r-9.9993836e-01 3.62e-01 6.51e+02 -3.8 6.48e+01 -3.9 1.47e-02
> 1.27e-02f 1
> 65r-9.9993423e-01 3.50e-01 6.14e+02 -3.8 2.19e+01 -3.4 5.80e-02
> 5.73e-02f 1
> 66r-9.9992087e-01 3.80e-01 5.83e+02 -3.8 7.47e+01 -3.9 3.31e-02
> 3.71e-02f 1
> 67r-9.9990091e-01 4.16e-01 5.64e+02 -3.8 3.72e+02 -4.4 4.91e-03
> 7.29e-03f 1
> 68r-9.9987230e-01 4.43e-01 5.25e+02 -3.8 6.51e+01 -4.0 3.35e-02
> 4.63e-02f 1
> 69r-9.9985833e-01 4.47e-01 5.30e+02 -3.8 4.13e+02 -4.4 3.63e-03
> 2.39e-03f 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
> alpha_pr ls
> 70r-9.9983957e-01 4.46e-01 5.33e+02 -3.8 7.49e+01 -4.0 3.36e-02
> 1.62e-02f 1
> 71r-9.9982788e-01 4.34e-01 4.87e+02 -3.8 2.08e+01 -3.6 1.91e-01
> 3.11e-02f 1
> 72r-9.9961339e-01 5.12e-01 4.49e+02 -3.8 1.08e+02 -4.1 2.44e-02
> 4.26e-02f 1
> 73r-9.9888965e-01 4.92e-01 4.21e+02 -3.8 2.83e+01 -3.6 4.49e-02
> 8.24e-02f 1
> 74r-9.9594603e-01 4.82e-01 3.76e+02 -3.8 1.03e+01 -3.2 1.07e-01
> 2.10e-02f 1
> 75r-9.8563504e-01 4.74e-01 3.72e+02 -3.8 3.30e+01 -3.7 7.35e-03
> 1.85e-02f 1
> 76r-9.6602124e-01 4.78e-01 4.24e+02 -3.8 1.62e+03 -4.2 3.99e-03
> 6.00e-04f 1
> 77r-9.1967458e-01 4.73e-01 3.95e+02 -3.8 4.25e+01 -3.7 8.24e-02
> 5.53e-02f 1
> 78r-9.1347771e-01 4.73e-01 3.93e+02 -3.8 5.10e+03 - 4.36e-03
> 2.83e-03f 1
> 79r-9.1206077e-01 4.71e-01 3.84e+02 -3.8 3.21e+03 - 1.32e-02
> 2.88e-03f 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
> alpha_pr ls
> 80r-9.0883354e-01 4.71e-01 3.81e+02 -3.8 4.04e+03 - 5.93e-03
> 5.70e-03f 1
> 81r-8.9924039e-01 5.07e-01 3.85e+02 -3.8 8.49e+01 -4.2 2.01e-02
> 4.63e-02f 1
> 82r-8.9828197e-01 5.02e-01 3.23e+02 -3.8 4.95e+01 -3.8 1.23e-01
> 1.59e-02f 1
> 83r-8.9776639e-01 5.02e-01 3.48e+02 -3.8 5.53e+02 -4.3 1.03e-02
> 1.10e-03f 1
> 84r-8.9102397e-01 4.86e-01 3.29e+02 -3.8 1.85e+03 - 1.99e-01
> 5.14e-02f 1
> 85r-8.6864981e-01 4.71e-01 2.99e+02 -3.8 1.49e+03 - 3.67e-01
> 2.39e-01f 1
> 86r-8.5214696e-01 4.41e-01 1.77e+02 -3.8 9.53e+02 - 2.36e-01
> 3.32e-01f 1
> 87r-8.4226320e-01 3.87e-01 1.39e+02 -3.8 6.26e+02 - 1.96e-01
> 2.83e-01f 1
> 88r-8.3979619e-01 3.56e-01 1.31e+02 -3.8 4.66e+02 - 3.50e-01
> 9.65e-02f 1
> 89r-8.3774544e-01 3.21e-01 2.46e+02 -3.8 4.44e+02 - 7.62e-01
> 1.14e-01f 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
> alpha_pr ls
> 90r-8.3200491e-01 2.37e-01 1.38e+02 -3.8 4.13e+02 - 6.65e-01
> 5.43e-01f 1
> 91r-8.2901673e-01 1.40e-01 8.35e+01 -3.8 2.02e+02 - 1.00e+00
> 5.38e-01f 1
> 92r-8.2921460e-01 1.06e-01 1.14e+02 -3.8 1.00e+02 - 1.00e+00
> 2.51e-01h 1
> 93r-8.2955368e-01 5.54e-02 5.91e+01 -3.8 7.36e+01 - 1.00e+00
> 4.92e-01h 1
> 94r-8.2990577e-01 1.95e-03 2.20e-02 -3.8 3.68e+01 - 1.00e+00
> 1.00e+00h 1
> 95r-8.2990498e-01 3.82e-05 5.43e-06 -3.8 1.45e-01 - 1.00e+00
> 1.00e+00h 1
> 96r-8.2931348e-01 6.84e-03 5.34e+02 -5.7 8.20e+01 - 8.92e-01
> 1.11e-01f 1
> 97r-8.2720401e-01 1.11e-02 2.26e+02 -5.7 2.67e+00 -4.8 1.00e+00
> 7.23e-01f 1
> 98r-8.2773815e-01 3.23e-01 7.18e+00 -5.7 2.49e+02 - 1.00e+00
> 9.71e-01f 1
> 99r-8.2797426e-01 8.68e-02 3.62e+00 -5.7 5.57e+01 - 1.00e+00
> 7.86e-01h 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
> alpha_pr ls
> 100r-8.2792610e-01 1.55e-03 4.01e-03 -5.7 8.59e+01 - 1.00e+00
> 1.00e+00h 1
> 101r-8.2806412e-01 2.67e-03 1.13e+03 -5.7 1.05e+05 - 9.30e-01
> 2.33e-01H 1
> 102r-8.2805242e-01 2.43e-03 1.03e+02 -5.7 1.86e-01 -4.8 1.00e+00
> 9.12e-02h 1
> 103r-8.2798281e-01 2.89e-05 1.20e-03 -5.7 1.18e+02 - 1.00e+00
> 1.00e+00f 1
> 104 -8.1217919e-01 2.06e+02 1.63e+02 -2.5 1.40e+06 - 1.96e-02
> 6.94e-01f 1
> 105 -8.0621917e-01 1.28e+02 6.38e+01 -2.5 7.20e+03 - 7.75e-01
> 3.81e-01f 1
> 106 -8.0017436e-01 8.01e-01 5.37e+01 -2.5 2.12e+03 - 1.00e+00
> 1.00e+00f 1
> 107 -8.0136084e-01 1.58e-02 8.12e-02 -2.5 2.08e+03 - 1.00e+00
> 1.00e+00h 1
> 108 -8.0135849e-01 3.90e-05 3.86e-05 -2.5 2.16e+01 - 1.00e+00
> 1.00e+00h 1
> 109 -8.0135849e-01 1.46e-09 1.61e-04 -3.8 5.54e-03 - 1.00e+00
> 1.00e+00h 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
> alpha_pr ls
> 110 -8.0135849e-01 1.44e-09 1.77e-06 -5.7 1.33e-01 - 1.00e+00
> 1.00e+00h 1
> 111 -8.0135973e-01 3.27e-07 4.83e-02 -8.6 2.41e+01 - 4.53e-01
> 1.00e+00h 1
> 112 -8.0135973e-01 1.53e-09 5.13e-08 -8.6 9.02e-06 -2.2 1.00e+00
> 1.00e+00h 1
> 113 -8.0321124e-01 2.12e+01 1.84e-04 -8.6 3.61e+04 - 1.22e-03
> 1.00e+00f 1
> 114 -8.0931322e-01 7.45e+01 4.34e-01 -8.6 1.30e+05 - 1.00e+00
> 1.00e+00h 1
> 115 -8.0856770e-01 5.34e-03 8.63e+00 -8.6 3.53e+00 -2.7 1.00e+00
> 1.00e+00h 1
> 116 -8.0860260e-01 4.13e-05 2.56e-01 -8.6 2.15e+02 - 1.00e+00
> 1.00e+00h 1
> 117 -8.2395907e-01 1.90e+02 7.36e-01 -8.6 4.12e+05 - 4.05e-01
> 1.00e+00h 1
> 118 -8.1858118e-01 3.06e-01 4.15e+02 -8.6 2.31e+01 -3.2 1.00e+00
> 1.00e+00h 1
> 119 -8.2020723e-01 6.29e-02 1.56e+02 -8.6 1.18e+04 - 1.00e+00
> 1.00e+00h 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
> alpha_pr ls
> 120 -8.2025508e-01 1.71e-03 5.62e-01 -8.6 2.11e+03 - 1.00e+00
> 1.00e+00h 1
> 121 -8.2300225e-01 3.34e+01 2.92e-02 -8.6 1.20e+05 - 1.00e+00
> 1.00e+00h 1
> 122 -8.2939602e-01 6.56e+01 2.73e-02 -8.6 2.15e+06 - 3.25e-01
> 1.45e-01h 1
> 123 -8.2655374e-01 1.52e+01 1.80e-03 -8.6 1.03e+05 - 1.00e+00
> 1.00e+00h 1
> 124 -8.2731976e-01 1.55e+00 2.75e-01 -8.6 3.44e+04 - 1.00e+00
> 1.00e+00h 1
> 125 -8.2731059e-01 5.22e-06 2.03e-03 -8.6 2.37e-02 -3.7 1.00e+00
> 1.00e+00h 1
> 126 -8.2780233e-01 4.17e-01 1.93e-02 -8.6 2.94e+04 - 1.00e+00
> 1.00e+00h 1
> 127 -8.2779746e-01 1.08e-06 3.29e-04 -8.6 2.03e-02 -4.2 1.00e+00
> 1.00e+00h 1
> 128 -8.2842776e-01 7.94e-01 7.13e-03 -8.6 1.04e+05 - 1.00e+00
> 3.74e-01h 1
> 129 -8.2825699e-01 1.14e+00 3.50e-03 -8.6 1.06e+04 - 1.00e+00
> 1.00e+00h 1
> iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du
> alpha_pr ls
> 130 -8.2841645e-01 5.95e-01 6.99e-06 -8.6 9.92e+03 - 1.00e+00
> 1.00e+00h 1
> 131 -8.2842603e-01 1.01e-04 3.94e-08 -8.6 6.30e+02 - 1.00e+00
> 1.00e+00h 1
> 132 -8.2842603e-01 1.02e-09 4.36e-12 -8.6 2.40e-02 - 1.00e+00
> 1.00e+00h 1
>
> Number of Iterations....: 132
>
> (scaled) (unscaled)
> Objective...............: -8.2842602716908775e-01 -8.2842602716908775e-01
> Dual infeasibility......: 4.3639707279903634e-12 4.3639707279903634e-12
> Constraint violation....: 2.9491946928281799e-11 1.0161187447010889e-09
> Complementarity.........: 2.5059035596805626e-09 2.5059035596805626e-09
> Overall NLP error.......: 2.5059035596805626e-09 2.5059035596805626e-09
>
>
> Number of objective function evaluations = 156
> Number of objective gradient evaluations = 42
> Number of equality constraint evaluations = 156
> Number of inequality constraint evaluations = 0
> Number of equality constraint Jacobian evaluations = 134
> Number of inequality constraint Jacobian evaluations = 0
> Number of Lagrangian Hessian evaluations = 132
> Total CPU secs in IPOPT (w/o function evaluations) = 2342.303
> Total CPU secs in NLP function evaluations = 235.838
>
> EXIT: Optimal Solution Found.
>
> Ipopt 3.11: Optimal Solution Found
> _______________________________________________
> Ipopt mailing list
> Ipopt at list.coin-or.org
> http://list.coin-or.org/mailman/listinfo/ipopt
>
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