[Ipopt] Ipopt converges not to desired point

[Илья Палачев]

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