[Ipopt] Ipopt converges not to desired point

Илья Палачев iliyapalachev at gmail.com
Tue Aug 12 11:51:15 EDT 2014


Thank you for paying attention to this issue.

There are so many options in Ipopt, that it seems to me that I launch it not with proper ones :)

Problem is

 minimize || h - h0 ||^2
 subject to Q h >= 0

The first doubt appears when Ipopt jumps to a big distance at the first step of the algorithm:

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
   0  8.8284119e+03 0.00e+00 6.49e+00  -1.0 0.00e+00    -  0.00e+00 0.00e+00   0
   1  7.7176010e+03 1.51e+03 6.03e+00  -1.0 1.07e+01    -  7.20e-02 6.97e-02f  1

My data is such that the precision of h and h0 must be near 1e-3 and the log says that we have ||d|| = 1.07e+01 at first step.
I expect that the step should be small, because from the geometric interpretation the local minimum should be located not far from the initial value.

Second doubt appears when I multiply both h and h0 on 1e3:

h *= 1e3
h0 *= 1e3

and Ipopt cannot converge in this case:

2997r 1.9123061e+08 2.93e-04 6.99e+02  -8.6 3.76e+02    -  2.84e-04 2.93e-04f  1
2998r 1.9123191e+08 2.93e-04 6.99e+02  -8.6 3.20e+02    -  1.50e-04 2.17e-05f  1
2999r 1.9124409e+08 2.93e-04 6.99e+02  -8.6 2.90e+02    -  6.76e-05 2.03e-04f  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du alpha_pr  ls
3000r 1.9124931e+08 2.93e-04 6.99e+02  -8.6 3.02e+02    -  2.35e-04 8.64e-05f  1

Number of Iterations....: 3000

                                   (scaled)                 (unscaled)
Objective...............:   2.8625304530690177e+06    1.9124930832628348e+08
Dual infeasibility......:   3.8009236804607247e+02    2.5394455598183948e+04
Constraint violation....:   2.9264571801934121e-04    2.9264571801934121e-04
Complementarity.........:   1.8743536898606338e-06    1.2522795918566969e-04
Overall NLP error.......:   3.8009236804607247e+02    2.5394455598183948e+04

Number of objective function evaluations             = 3006
Number of objective gradient evaluations             = 1495
Number of equality constraint evaluations            = 0
Number of inequality constraint evaluations          = 3006
Number of equality constraint Jacobian evaluations   = 0
Number of inequality constraint Jacobian evaluations = 3002
Number of Lagrangian Hessian evaluations             = 3000
Total CPU secs in IPOPT (w/o function evaluations)   =     86.717
Total CPU secs in NLP function evaluations           =      7.000

EXIT: Maximum Number of Iterations Exceeded.

09.07.2014, 22:44, "Wei Wan" <weiwan at andrew.cmu.edu>:
>  From the output log, there is nothing wrong with IPOPT. The problem is well proposed and pretty easy to solve.
>  If I understood your question correctly, IPOPT is expected to converge to another local optimal solution which is close to zero. Then you can try some other starting points like h0.
>  By the way, you metioned
>  "In function "eval_g" the vector Q * x is computed.
>  In function "eval_jac_g" the matrix Q is computed."
>  Does it imply that Q isn't a function of x? Then
>  minimize || h - h0 ||^2
>  subject to Q h >= 0
>  is a convex QP with only one optimal solution. I am confused with this issue.
>  On Wed, Jul 9, 2014 at 10:01 AM, Илья Палачев <iliyapalachev at gmail.com> wrote:
>>  <div><div>09.07.2014, 17:59, "Илья Палачев" <palachev.ilya at yandex.ru>: ></div><div>Hi, all.</div><div>&nbsp;</div><div>I'm using Ipopt via C++ interface to solve the following problem:</div><div>&nbsp;</div><div>minimize || h - h0 ||^2</div><div>&nbsp;</div><div>subject to Q h >= 0</div><div>&nbsp;</div><div>where h0 (known) and h (unknown) is vector of dimension N and Q is M x N matrix.</div><div>&nbsp;</div><div>Q is always very sparse: it has only 4 non-zero elements in each row. Also we know that its rank is always (N - 3) and 3 basis vectors of its kernel are known beforehand (a priori).</div><div>&nbsp;</div><div>Usually N ~ 5000 and M ~ 15000. From empirical knowledge we are expecting that minimal value of the functional must be near 0, because vector h0 lies closely to the set {Q h >= 0}</div><div>&nbsp;</div><div>But Ipopt converges in 1-2 seconds to the point where this value is too big.</div><div>&nbsp;</div><div>I set tolerance values as follows:</div><div>&nbsp;</div><div>&nbsp; &nbsp; app->Options()->SetNumericValue("tol", 1e! > &nbsp;-10);</div><div>&nbsp; &nbsp; app->Options()->SetNumericValue("acceptable_tol", 1e-10);</div><div>&nbsp;</div><div>In function "get_starting_point" starting point is set to (1, 1, ..., 1) - it always lies inside the set {Q h >= 0}</div><div>In function "eval_g" the vector Q * x is computed.</div><div>In function "eval_jac_g" the matrix Q is computed</div><div>In function "eval_h" the matrix 2 * obj_value * I is computed, where I is the identity matrix.</div><div>&nbsp;</div><div>Can you clarify the following questions:</div><div>&nbsp
>>  ;</div><div>1. Am I using Iptopt correctly for this problem?</div><div>2. Are there any possible options/modes that can help to avoid this problem?</div><div>3. Or the problem is infeasible itself? How can I reformulate it to be able to obtain appropriate solution?</div><div>&nbsp;</div><div>Here is the log from Ipopt:</div><div>&nbsp;</div><div>******************************************************************************</div><div>Th! > &nbsp;is program contains Ipopt, a library for large-scale nonlinear optimiza > tion.</div><div>Ipopt is released as open source code under the Eclipse Public License (EPL).</div><div>&nbsp; &nbsp; &nbsp; &nbsp; For more information visit http://projects.coin-or.org/Ipopt</div><div>******************************************************************************</div><div>&nbsp;</div><div>This is Ipopt version 3.11.7, running with linear solver ma27.</div><div>&nbsp;</div><div>Number of nonzeros in equality constraint Jacobian...:&nbsp; &nbsp; &nbsp; &nbsp; 0</div><div>Number of nonzeros in inequality constraint Jacobian.:&nbsp; &nbsp; 14456</div><div>Number of nonzeros in Lagrangian Hessian.............:&nbsp; &nbsp; 1240</div><div>&nbsp;</div><div>Total number of variables............................:&nbsp; &nbsp; 1240</div><div>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; variables with only lower bounds:&nbsp; &nbsp; &nbsp; &nbsp; 0</div><div>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; variables with lower and upper! > &nbsp;&nbsp;bounds:&nbsp; &nbsp; &nbsp; &nbsp; 0</div><div>&nbs
>>  p; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; variables with only upper bounds:&nbsp; &nbsp; &nbsp; &nbsp; 0</div><div>Total number of equality constraints.................:&nbsp; &nbsp; &nbsp; &nbsp; 0</div><div>Total number of inequality constraints...............:&nbsp; &nbsp; 3614</div><div>&nbsp; &nbsp; &nbsp; &nbsp; inequality constraints with only lower bounds:&nbsp; &nbsp; 3614</div><div>&nbsp; inequality constraints with lower and upper bounds:&nbsp; &nbsp; &nbsp; &nbsp; 0</div><div>&nbsp; &nbsp; &nbsp; &nbsp; inequality constraints with only upper bounds:&nbsp; &nbsp; &nbsp; &nbsp; 0</div><div>&nbsp;</div><div>iter&nbsp; &nbsp; objective&nbsp; &nbsp; inf_pr&nbsp; inf_du lg(mu)&nbsp; ||d||&nbsp; lg(rg) alpha_du alpha_pr&nbsp; ls</div><div>&nbsp; 0&nbsp; 1.8336107e+03 0.00e+00 1.05e+01&nbsp; -1.0 0.00e+00&nbsp; &nbsp; -&nbsp; 0.00e+00 0.00e+00&nbsp; 0</div><div>&nbsp; 1&nbsp; 1.6674085e+03 9.38e! > &nbsp;-03 9.96e+00&nbsp; -1.0 4.94e+00&nbsp; &nbsp; -&nbsp; 8.49e-02 4.82e-02 > f&nbsp; 1</div><div>&nbsp; 2&nbsp; 1.4326345e+03 8.72e-03 3.33e+01&nbsp; -1.0 4.92e+00&nbsp; &nbsp; -&nbsp; 3.41e-01 7.77e-02f&nbsp; 1</div><div>&nbsp; 3&nbsp; 1.2617809e+03 8.15e-03 9.36e+01&nbsp; -1.0 4.17e+00&nbsp; &nbsp; -&nbsp; 3.21e-01 6.85e-02f&nbsp; 1</div><div>&nbsp; 4&nbsp; 1.0488307e+03 7.32e-03 4.45e+02&nbsp; -1.0 3.88e+00&nbsp; &nbsp; -&nbsp; 6.88e-01 1.04e-01f&nbsp; 1</div><div>&nbsp; 5&nbsp; 7.8339830e+02 6.00e-03 6.15e+02&nbsp; -1.0 3.48e+00&nbsp; &nbsp; -&nbsp; 1.00e+00 1.77e-01f&nbsp
>>  ; 1</div><div>&nbsp; 6&nbsp; 6.2985014e+02 4.97e-03 9.84e+02&nbsp; -1.0 2.86e+00&nbsp; &nbsp; -&nbsp; 9.01e-01 1.73e-01f&nbsp; 1</div><div>&nbsp; 7&nbsp; 5.3144166e+02 3.94e-03 2.42e+03&nbsp; -1.0 2.37e+00&nbsp; &nbsp; -&nbsp; 1.00e+00 2.08e-01f&nbsp; 1</div><div>&nbsp; 8&nbsp; 4.9770694e+02 3.07e-03 1.94e+03&nbsp; -1.0 1.87e+00&nbsp; &nbsp; -&nbsp; 5.86e-01 2.21e-01h&nbsp; 1</div><div>&nbsp; 9&nbsp; 5.0406399e+02 2.54e-03 2.45e+03&nbsp; -1.0 2.11e+00&nbsp; &nbsp; -&nbsp; 5.80e-! > &nbsp;01 1.73e-01h&nbsp; 1</div><div>iter&nbsp; &nbsp; objective&nbsp; &nbsp; inf_pr&nbsp; inf_du lg(mu)&nbsp; ||d||&nbsp; lg(rg) alpha_du alpha_pr&nbsp; ls</div><div>&nbsp; 10&nbsp; 5.3547390e+02 2.00e-03 3.58e+03&nbsp; -1.0 1.99e+00&nbsp; &nbsp; -&nbsp; 5.68e-01 2.12e-01h&nbsp; 1</div><div>&nbsp; 11&nbsp; 5.9274922e+02 1.48e-03 5.87e+03&nbsp; -1.0 2.28e+00&nbsp; &nbsp; -&nbsp; 1.00e+00 2.56e-01h&nbsp; 1</div><div>&nbsp; 12&nbsp; 6.4631623e+02 1.20e-03 9.56e+03&nbsp; -1.0 2.88e+00&nbsp; &nbsp; -&nbsp; 7.47e-01 1.91e-01h&nbsp; 1</div><div>&nbsp; 13&nbsp; 7.1841000e+02 9.18e-04 9.95e+03&nbsp; -1.0 2.29e+00&nbsp; &nbsp; -&nbsp; 1.00e+00 2.36e-01h&nbsp; 1</div><div>&nbsp; 14&nbsp; 8.1146204e+02 6.58e-04 1.56e+04&nbsp; -1.0 2.23e+00&nbsp; &nbsp; -&nbsp; 8.62e-01 2.83e-01h&nbsp; 1</div><div>&nbsp; 15&nbsp; 8.8773763e+02 5.02e-04 1.40e+04&nbsp; -1.0 2.02e+00&nbsp; &nbsp; -&nbsp; 1.00e+00 2.38e-01h&nbsp; 1</div><div>&nbsp; 16&nbsp; 9.5457040e+02 3.99e-04 3.42e+04&nbsp; -1.0 2.57e+00&nbs! > &nbsp;p; &nbsp; -&nbsp; 1.00e+00 2.07e-01h&nbsp; 1</div>&lt
>>  ;div>&nbsp; 17&nbsp; > 1.0558386e+03 2.78e-04 2.99e+04&nbsp; -1.0 2.83e+00&nbsp; &nbsp; -&nbsp; 1.00e+00 3.02e-01h&nbsp; 1</div><div>&nbsp; 18&nbsp; 1.1619864e+03 1.84e-04 2.61e+04&nbsp; -1.0 2.36e+00&nbsp; &nbsp; -&nbsp; 1.00e+00 3.38e-01h&nbsp; 1</div><div>&nbsp; 19&nbsp; 1.2303388e+03 1.37e-04 2.72e+04&nbsp; -1.0 1.75e+00&nbsp; &nbsp; -&nbsp; 1.00e+00 2.56e-01h&nbsp; 1</div><div>iter&nbsp; &nbsp; objective&nbsp; &nbsp; inf_pr&nbsp; inf_du lg(mu)&nbsp; ||d||&nbsp; lg(rg) alpha_du alpha_pr&nbsp; ls</div><div>&nbsp; 20&nbsp; 1.3150608e+03 9.06e-05 6.56e+04&nbsp; -1.0 3.25e+00&nbsp; &nbsp; -&nbsp; 8.83e-01 3.36e-01h&nbsp; 1</div><div>&nbsp; 21&nbsp; 1.3814642e+03 6.27e-05 7.75e+04&nbsp; -1.0 2.40e+00&nbsp; &nbsp; -&nbsp; 7.12e-01 3.08e-01h&nbsp; 1</div><div>&nbsp; 22&nbsp; 1.4350326e+03 4.50e-05 5.61e+04&nbsp; -1.0 3.49e+00&nbsp; &nbsp; -&nbsp; 2.96e-01 2.84e-01h&nbsp; 1</div><div>&nbsp; 23&nbsp; 1.4589438e+03 3.83e-05 5.49e+04&nbsp; -1.0 1.99e+00&nbsp; &nbsp; -&nbsp; 3.16e-01 1.50e-01h&nbsp; 1 &nbsp;v><div>&nbsp; 24&nbsp; 1.5206104e+03 2.37e-05 7.37e+04&nbsp; -1.0 2.93e+00&nbsp; &nbsp; -&nbsp; 5.14e-01 3.78e-01h&nbsp; 1</div><div>&nbsp; 25&nbsp; 1.5669190e+03 1.50e-05 1.31e+05&nbsp; -1.0 1.86e+00&nbsp; &nbsp; -&nbsp; 7.69e-01 3.67e-01h&nbsp; 1</div><div>&nbsp; 26&nbsp; 1.5903011e+03 1.12e-05 1.13e+05&nbsp; -1.0 1.21e+00&nbsp; &nbsp; -&nbsp; 1.00e+00 2.57e-01h&nbsp; 1</div><div>&nbsp; 27&nbsp; 1.6230534e+03 6.42e-06 1.53e+05&nbsp; -1.0 1.28e+00&nbsp; &nbsp; -&nbsp; 1.00e+00 4.23e-01h&nbsp; 1</div><div>&nbsp; 28&nbsp; 1.64740
>>  62e+03 3.44e-06 8.28e+04&nbsp; -1.0 1.36e+00&nbsp; &nbsp; -&nbsp; 4.38e-01 4.63e-01h&nbsp; 1</div><div>&nbsp; 29&nbsp; 1.6522123e+03 2.93e-06 8.53e+05&nbsp; -1.0 9.59e-01&nbsp; &nbsp; -&nbsp; 1.00e+00 1.54e-01h&nbsp; 1</div><div>iter&nbsp; &nbsp; objective&nbsp; &nbsp; inf_pr&nbsp; inf_du lg(mu)&nbsp; ||d||&nbsp; lg(rg) alpha_du alpha_pr&nbsp; ls</div><div>&nbsp; 30&nbsp; 1.6718478e+03 9.85e-07 3.39e+05&nbsp; -1.0 1.03e+00&nbsp; &nbsp; -&nbsp; 7.48e-! > &nbsp;01 6.32e-01h&nbsp; 1</div><div>&nbsp; 31&nbsp; 1.6799887e+03 4.29e-07 1 > .41e+05&nbsp; -1.0 3.88e-01&nbsp; &nbsp; -&nbsp; 4.78e-01 5.95e-01h&nbsp; 1</div><div>&nbsp; 32&nbsp; 1.6840614e+03 2.54e-07 3.89e+05&nbsp; -1.0 1.94e-01&nbsp; &nbsp; -&nbsp; 5.80e-01 3.34e-01h&nbsp; 1</div><div>&nbsp; 33&nbsp; 1.6930559e+03 9.47e-08 1.70e+05&nbsp; -1.0 2.36e-01&nbsp; &nbsp; -&nbsp; 6.41e-01 6.19e-01h&nbsp; 1</div><div>&nbsp; 34&nbsp; 1.6978451e+03 6.91e-08 1.21e+06&nbsp; -1.0 2.57e-01&nbsp; &nbsp; -&nbsp; 6.02e-01 3.72e-01h&nbsp; 1</div><div>&nbsp; 35&nbsp; 1.7068217e+03 1.90e-08 1.64e+06&nbsp; -1.0 2.56e-01&nbsp; &nbsp; -&nbsp; 9.22e-01 6.22e-01h&nbsp; 1</div><div>MA27BD returned iflag=-4 and requires more memory.</div><div>Increase liw from 223615 to 447230 and la from 262915 to 535470 and factorize again.</div><div>&nbsp; 36&nbsp; 1.7162980e+03 6.31e-09 2.18e+06&nbsp; -1.0 2.17e-01&nbsp; &nbsp; -&nbsp; 1.00e+00 7.52e-01h&nbsp; 1</div><div>&nbsp; 37&nbsp; 1.7233855e+03 0.00e+00 1.00e-06&nbsp; -1.0 1.19e-01&nbsp; &nbsp; -&nbsp; 1.00e+00 1.00e+00h&nbsp; 1 &nbsp;div><div>&nbsp; 38&nbsp; 1.6800304e+0
>>  3 0.00e+00 1.83e+07&nbsp; -8.6 9.78e-01&nbsp; &nbsp; -&nbsp; 4.83e-01 1.00e+00f&nbsp; 1</div><div>&nbsp; 39&nbsp; 1.6758852e+03 0.00e+00 1.04e+07&nbsp; -8.6 3.02e-01&nbsp; &nbsp; -&nbsp; 4.26e-01 5.67e-01f&nbsp; 1</div><div>iter&nbsp; &nbsp; objective&nbsp; &nbsp; inf_pr&nbsp; inf_du lg(mu)&nbsp; ||d||&nbsp; lg(rg) alpha_du alpha_pr&nbsp; ls</div><div>&nbsp; 40&nbsp; 1.6735636e+03 0.00e+00 7.19e+06&nbsp; -8.6 2.16e-01&nbsp; &nbsp; -&nbsp; 2.98e-01 3.68e-01f&nbsp; 1</div><div>&nbsp; 41&nbsp; 1.6718941e+03 0.00e+00 5.63e+06&nbsp; -8.6 1.91e-01&nbsp; &nbsp; -&nbsp; 2.09e-01 2.60e-01f&nbsp; 1</div><div>&nbsp; 42&nbsp; 1.6702121e+03 0.00e+00 4.53e+06&nbsp; -8.6 1.59e-01&nbsp; &nbsp; -&nbsp; 1.81e-01 2.74e-01f&nbsp; 1</div><div>&nbsp; 43&nbsp; 1.6682895e+03 0.00e+00 3.33e+06&nbsp; -8.6 1.53e-01&nbsp; &nbsp; -&nbsp; 2.53e-01 3.45e-01f&nbsp; 1</div><div>&nbsp; 44&nbsp; 1.6669311e+03 0.00e+00 2.16e+06&nbsp; -8.6 1.31e-01&nbsp; &nbsp; -&nbsp; 3.53! > &nbsp;e-01 2.95e-01f&nbsp; 1</div><div>&nbsp; 45&nbsp; 1.6657351e+03 0.00e+00 > &nbsp;2.01e+06&nbsp; -8.6 1.15e-01&nbsp; &nbsp; -&nbsp; 8.36e-02 3.20e-01f&nbsp; 1</div><div>&nbsp; 46&nbsp; 1.6652164e+03 0.00e+00 1.67e+06&nbsp; -8.6 8.89e-02&nbsp; &nbsp; -&nbsp; 1.73e-01 1.84e-01f&nbsp; 1</div><div>&nbsp; 47&nbsp; 1.6645884e+03 0.00e+00 9.83e+05&nbsp; -8.6 8.30e-02&nbsp; &nbsp; -&nbsp; 4.02e-01 2.51e-01f&nbsp; 1</div><div>&nbsp; 48&nbsp; 1.6639691e+03 0.00e+00 7.19e+05&nbsp; -8.6 7.43e-02&nbsp; &nbsp; -&nbsp; 2.68e-01 2.77e-01f&nbsp; 1</div><div>&nbsp; 49&nbsp; 1.6635414e+03 0.00e+00 5.42e
>>  +05&nbsp; -8.6 6.52e-02&nbsp; &nbsp; -&nbsp; 2.49e-01 2.28e-01f&nbsp; 1</div><div>iter&nbsp; &nbsp; objective&nbsp; &nbsp; inf_pr&nbsp; inf_du lg(mu)&nbsp; ||d||&nbsp; lg(rg) alpha_du alpha_pr&nbsp; ls</div><div>&nbsp; 50&nbsp; 1.6630697e+03 0.00e+00 4.13e+05&nbsp; -8.6 5.94e-02&nbsp; &nbsp; -&nbsp; 2.42e-01 2.99e-01f&nbsp; 1</div><div>&nbsp; 51&nbsp; 1.6628218e+03 0.00e+00 3.30e+05&nbsp; -8.6 4.72e-02&nbsp; &nbsp; -&nbsp; 3.61e-01 2.09e-01f&nbsp; 1</div><div>&nbsp; 52&nbsp;! > &nbsp;&nbsp;1.6626052e+03 0.00e+00 2.65e+05&nbsp; -8.6 4.32e-02&nbsp; &nbsp; -&nbsp; 2.12e-01 2.31e-01f&nbsp; 1</div><div>&nbsp; 53&nbsp; 1.6623597e+03 0.00e+00 1.36e+05&nbsp; -8.6 3.52e-02&nbsp; &nbsp; -&nbsp; 4.54e-01 3.33e-01f&nbsp; 1</div><div>&nbsp; 54&nbsp; 1.6622941e+03 0.00e+00 1.17e+05&nbsp; -8.6 2.24e-02&nbsp; &nbsp; -&nbsp; 1.57e-01 1.33e-01f&nbsp; 1</div><div>&nbsp; 55&nbsp; 1.6621419e+03 0.00e+00 9.82e+04&nbsp; -8.6 1.60e-02&nbsp; &nbsp; -&nbsp; 2.22e-01 3.49e-01f&nbsp; 1</div><div>&nbsp; 56&nbsp; 1.6620561e+03 0.00e+00 5.31e+04&nbsp; -8.6 9.62e-03&nbsp; &nbsp; -&nbsp; 3.70e-01 3.16e-01f&nbsp; 1</div><div>&nbsp; 57&nbsp; 1.6620052e+03 0.00e+00 3.80e+04&nbsp; -8.6 4.76e-03&nbsp; &nbsp; -&nbsp; 2.71e-01 2.86e-01f&nbsp; 1</div><div>&nbsp; 58&nbsp; 1.6619647e+03 0.00e+00 2.57e+04&nbsp; -8.6 2.65e-03&nbsp; &nbsp; -&nbsp; 4.19e-01 3.17e-01f&nbsp; 1</div><div>&nbsp; 59&nbsp; 1.6619354e+03 0.00e+00 2.82e+04&nbsp; -8.6 1.87e-03&nbsp; &nbsp; -&nbsp; 4.09e-01 3.26e-01f&nbsp; 1</div>! > &nbsp;<div>iter&nbsp; &nbsp; objective&nbsp; &nbsp;
>>  inf_pr&nbsp; inf_du lg(mu > )&nbsp; ||d||&nbsp; lg(rg) alpha_du alpha_pr&nbsp; ls</div><div>&nbsp; 60&nbsp; 1.6619094e+03 0.00e+00 1.35e+04&nbsp; -8.6 1.36e-03&nbsp; &nbsp; -&nbsp; 3.19e-01 4.18e-01f&nbsp; 1</div><div>&nbsp; 61&nbsp; 1.6618945e+03 0.00e+00 2.92e+04&nbsp; -8.6 1.52e-03&nbsp; &nbsp; -&nbsp; 3.08e-01 4.05e-01f&nbsp; 1</div><div>&nbsp; 62&nbsp; 1.6618912e+03 0.00e+00 2.40e+04&nbsp; -8.6 1.57e-03&nbsp; &nbsp; -&nbsp; 4.88e-01 1.58e-01f&nbsp; 1</div><div>&nbsp; 63&nbsp; 1.6618823e+03 0.00e+00 7.96e+03&nbsp; -8.6 1.74e-03&nbsp; &nbsp; -&nbsp; 4.09e-01 4.93e-01f&nbsp; 1</div><div>&nbsp; 64&nbsp; 1.6618804e+03 0.00e+00 2.46e+04&nbsp; -8.6 1.03e-03&nbsp; &nbsp; -&nbsp; 5.08e-01 2.16e-01f&nbsp; 1</div><div>&nbsp; 65&nbsp; 1.6618764e+03 0.00e+00 1.11e+04&nbsp; -8.6 5.81e-04&nbsp; &nbsp; -&nbsp; 4.61e-01 5.75e-01f&nbsp; 1</div><div>&nbsp; 66&nbsp; 1.6618747e+03 0.00e+00 5.85e+03&nbsp; -8.6 3.44e-04&nbsp; &nbsp; -&nbsp; 5.02e-01 5.52e-01f&nbsp; 1</div><div>&nbsp; 67&nbsp; 1.6618739e+03 0.00e+00 3.00! > &nbsp;e+03&nbsp; -8.6 2.76e-04&nbsp; &nbsp; -&nbsp; 5.40e-01 6.14e-01f&nbsp; 1</div><div>&nbsp; 68&nbsp; 1.6618737e+03 0.00e+00 1.41e+03&nbsp; -8.6 2.09e-04&nbsp; &nbsp; -&nbsp; 5.28e-01 5.16e-01f&nbsp; 1</div><div>&nbsp; 69&nbsp; 1.6618736e+03 0.00e+00 3.96e+03&nbsp; -8.6 1.44e-04&nbsp; &nbsp; -&nbsp; 6.54e-01 4.50e-01f&nbsp; 1</div><div>iter&nbsp; &nbsp; objective&nbsp; &nbsp; inf_pr&nbsp; inf_du lg(mu)&nbsp; ||d||&nbsp; lg(rg) alpha_du alpha_pr&nbsp; ls</div><div>&nbsp; 70&nbsp; 1.6618735e+03 0.00e+00 4.37e+03&nbsp; -8.6 1.1
>>  3e-04&nbsp; &nbsp; -&nbsp; 7.15e-01 5.20e-01f&nbsp; 1</div><div>&nbsp; 71&nbsp; 1.6618734e+03 0.00e+00 1.37e+03&nbsp; -8.6 7.36e-05&nbsp; &nbsp; -&nbsp; 6.20e-01 7.01e-01f&nbsp; 1</div><div>&nbsp; 72&nbsp; 1.6618734e+03 0.00e+00 4.65e+02&nbsp; -8.6 3.41e-05&nbsp; &nbsp; -&nbsp; 1.00e+00 8.89e-01f&nbsp; 1</div><div>&nbsp; 73&nbsp; 1.6618734e+03 0.00e+00 7.28e-12&nbsp; -8.6 1.57e-05&nbsp; &nbsp; -&nbsp; 1.00e+00 1.00e+00f&nbsp; 1</div><div>&nbsp;</div><div>Nu! > &nbsp;mber of Iterations....: 73</div><div>&nbsp;</div><div>&nbsp; &nbsp; &nb > sp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (scaled)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (unscaled)</div><div>Objective...............:&nbsp; 1.6618734205379653e+03&nbsp; &nbsp; 1.6618734205379653e+03</div><div>Dual infeasibility......:&nbsp; 7.2759576141834259e-12&nbsp; &nbsp; 7.2759576141834259e-12</div><div>Constraint violation....:&nbsp; 0.0000000000000000e+00&nbsp; &nbsp; 0.0000000000000000e+00</div><div>Complementarity.........:&nbsp; 4.1913907266361601e-09&nbsp; &nbsp; 4.1913907266361601e-09</div><div>Overall NLP error.......:&nbsp; 1.5424634363936447e-11&nbsp; &nbsp; 4.1913907266361601e-09</div><div>&nbsp;</div><div>&nbsp;</div><div>Number of objective function evaluations&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 74</div><div>Number of objective gradient evaluations&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 74</div><div>Number of equality constraint evaluations&amp
>>  ;nbsp; &nbsp; &nbsp; &nbsp; ! > &nbsp;&nbsp; &nbsp; = 0</div><div>Number of inequality constraint evaluations&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 74</div><div>Number of equality constraint Jacobian evaluations&nbsp; = 0</div><div>Number of inequality constraint Jacobian evaluations = 74</div><div>Number of Lagrangian Hessian evaluations&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; = 73</div><div>Total CPU secs in IPOPT (w/o function evaluations)&nbsp; =&nbsp; &nbsp; &nbsp; 0.728</div><div>Total CPU secs in NLP function evaluations&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; =&nbsp; &nbsp; &nbsp; 0.032</div><div>&nbsp;</div><div>EXIT: Optimal Solution Found.</div><div>&nbsp;</div><div>&nbsp;</div><div>&nbsp;</div><div>Best regards,</div><div>&nbsp;</div><div>Ilya Palachev</div>> > _______________________________________________ > Ipopt mailing list > Ipopt at list.coin-or.org > http://list.coin-or.org/mailman/listinfo/ipopt</div></div></div>
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