<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<meta name="Generator" content="Microsoft Word 12 (filtered medium)">
<style>
<!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Consolas;
panose-1:2 11 6 9 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri","sans-serif";}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
span.E-MailFormatvorlage17
{mso-style-type:personal-compose;
font-family:"Calibri","sans-serif";
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;}
@page Section1
{size:612.0pt 792.0pt;
margin:70.85pt 70.85pt 2.0cm 70.85pt;}
div.Section1
{page:Section1;}
-->
</style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang="DE" link="blue" vlink="purple">
<div class="Section1">
<p class="MsoNormal"><span lang="EN-US">Hello,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">I am using IPOPT to solve the NLP arising in Nonlinear Model Predictive Control. IPOPT was compiled with MS Visual Studio 10 according to the documentation. In order to access IPOPT in MATLAB/Simulink the C Interface
is used. <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">At the starting point, the user-supplied hessian is indefinite (checked with MATLAB's chol(hessian)). According to the implementation IPOPT should add a multiple of the unity matrix to the indefinite hessian. Unfortunately
this is not done and the objective function is only reduced slightly. See the output :<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:12.0pt;
font-family:"Courier New""><o:p> </o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">List of user-set options:</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> </span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> Name Value used</span><span lang="EN-US" style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> hessian_approximation = exact yes</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> max_iter = 10 yes</span><span lang="EN-US" style="font-size:
12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> output_file = ipopt yes</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> print_user_options = yes yes</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> </span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">******************************************************************************</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">This program contains Ipopt, a library for large-scale nonlinear optimization.</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> Ipopt is released as open source code under the Eclipse Public License (EPL).</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> For more information visit http://projects.coin-or.org/Ipopt</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">******************************************************************************</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> </span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">This is Ipopt version 3.9stable, running with linear solver ma27.</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> </span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Number of nonzeros in equality constraint Jacobian...: 0</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Number of nonzeros in inequality constraint Jacobian.: 0</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Number of nonzeros in Lagrangian Hessian.............: 45150</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> </span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Total number of variables............................: 300</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> variables with only lower bounds: 0</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> variables with lower and upper bounds: 300</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> variables with only upper bounds: 0</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Total number of equality constraints.................: 0</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Total number of inequality constraints...............: 0</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> inequality constraints with only lower bounds: 0</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> inequality constraints with lower and upper bounds: 0</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> inequality constraints with only upper bounds: 0</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> </span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black">iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls</span><span style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black"> 0 9.8696044e+006 0.00e+000 1.00e+002 -1.0 0.00e+000 - 0.00e+000 0.00e+000 0</span><span style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black"> 1 9.2476193e+006 0.00e+000 9.65e+001 -1.0 1.43e+000 - 9.62e-001 1.00e+000f 1</span><span style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black"> 2 8.6650164e+006 0.00e+000 9.27e+001 -1.0 1.39e+000 - 1.00e+000 1.00e+000f 1</span><span style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black"> 3 8.1192261e+006 0.00e+000 8.87e+001 -1.0 1.21e+000 - 1.00e+000 1.00e+000f 1</span><span style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black"> 4 7.6084135e+006 0.00e+000 8.50e+001 -1.0 1.40e+000 - 1.00e+000 1.00e+000f 1</span><span style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black"> 5 7.1293098e+006 0.00e+000 8.17e+001 -1.0 1.24e+000 - 1.00e+000 1.00e+000f 1</span><span style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black"> 6 6.6799462e+006 0.00e+000 7.85e+001 -1.0 1.22e+000 - 1.00e+000 1.00e+000f 1</span><span style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black"> 7 6.2582696e+006 0.00e+000 7.55e+001 -1.0 1.22e+000 - 1.00e+000 1.00e+000f 1</span><span style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black"> 8 5.8623887e+006 0.00e+000 7.28e+001 -1.0 1.25e+000 - 1.00e+000 1.00e+000f 1</span><span style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black"> 9 5.4905752e+006 0.00e+000 7.04e+001 -1.0 1.33e+000 - 1.00e+000 1.00e+000f 1</span><span style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black">iter objective inf_pr inf_du lg(mu) ||d|| lg(rg) alpha_du alpha_pr ls</span><span style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black"> 10 5.1412512e+006 0.00e+000 6.84e+001 -1.0 1.40e+000 - 1.00e+000 1.00e+000f 1</span><span style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black"> </span><span style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black">Number of Iterations....: 10</span><span style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black"> </span><span style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span style="font-size:10.0pt;
font-family:"Courier New";color:black">
</span><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">(scaled) (unscaled)</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Objective...............: 1.6480135408498565e+005 5.1412511506722849e+006</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Dual infeasibility......: 6.8365045374688762e+001 2.1327608025424806e+003</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Constraint violation....: 0.0000000000000000e+000 0.0000000000000000e+000</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Complementarity.........: 1.0000000000036685e-001 3.1196655993735813e+000</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Overall NLP error.......: 6.8365045374688762e+001 2.1327608025424806e+003</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> </span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> </span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Number of objective function evaluations = 11</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Number of objective gradient evaluations = 11</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Number of equality constraint evaluations = 0</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Number of inequality constraint evaluations = 0</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Number of equality constraint Jacobian evaluations = 0</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Number of inequality constraint Jacobian evaluations = 0</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Number of Lagrangian Hessian evaluations = 10</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Total CPU secs in IPOPT (w/o function evaluations) = 0.148</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">Total CPU secs in NLP function evaluations = 4.480</span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black"> </span><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:10.0pt;font-family:"Courier New";color:black">EXIT: Maximum Number of Iterations Exceeded.</span><span lang="EN-US" style="font-size:12.0pt;
font-family:"Courier New""><o:p></o:p></span></p>
<p class="MsoNormal" style="text-autospace:none"><span lang="EN-US" style="font-size:12.0pt;font-family:"Courier New""><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">The same problem was also solved with MATLAB's fmincon. The gradient and hessian are exactly the same, but the result is different (see objective function):<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> First-order Norm of<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> Iter F-count f(x) Feasibility optimality step<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> </span>0 1 9.869604e+006 0.000e+000 3.117e+003<o:p></o:p></p>
<p class="MsoNormal"> 1 3 3.304693e+006 0.000e+000 2.153e+003 2.789e+002<o:p></o:p></p>
<p class="MsoNormal"> 2 4 1.474439e+006 0.000e+000 2.133e+003 1.759e+002<o:p></o:p></p>
<p class="MsoNormal"> 3 5 4.765775e+005 0.000e+000 1.655e+003 1.079e+002<o:p></o:p></p>
<p class="MsoNormal"> 4 6 1.159478e+005 0.000e+000 9.911e+002 9.736e+001<o:p></o:p></p>
<p class="MsoNormal"> 5 7 4.110189e+004 0.000e+000 6.411e+002 5.950e+001<o:p></o:p></p>
<p class="MsoNormal"> 6 8 1.365444e+004 0.000e+000 3.948e+002 5.898e+001<o:p></o:p></p>
<p class="MsoNormal"> 7 9 5.660985e+003 0.000e+000 2.668e+002 5.086e+001<o:p></o:p></p>
<p class="MsoNormal"> 8 10 2.314725e+003 0.000e+000 1.779e+002 5.414e+001<o:p></o:p></p>
<p class="MsoNormal"> 9 11 5.767229e+002 0.000e+000 9.207e+001 6.265e+001<o:p></o:p></p>
<p class="MsoNormal"> 10 12 3.626214e+001 0.000e+000 1.861e+001 7.382e+001<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Consolas">My questions are:<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:10.5pt;font-family:Consolas">1) Why does IPOPT not recognize the indefinite hessian matrix? What possible options might clear this problem? With the BFGS formula for the hessian everything works fine.
But we want to use the exact hessian.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:10.5pt;font-family:Consolas"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:10.5pt;font-family:Consolas">2) Does the warm start option also work with the C Interface?<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:10.5pt;font-family:Consolas"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:10.5pt;font-family:Consolas">Best Regards
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:10.5pt;font-family:Consolas">Simon</span><span style="font-size:10.5pt;font-family:Consolas"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Consolas"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Consolas">-----------------------------------------------------<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Consolas">Dipl.-Ing. Simon Altmannshofer<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Consolas">Lehrstuhl für Regelungstechnik<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Consolas">Technische Universität München<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Consolas">Boltzmannstraße 15<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Consolas">85748 Garching bei München<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Consolas"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Consolas">Tel.: +49 (89) 289-15679<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Consolas">Fax: +49 (89) 289-15653<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Consolas">E-Mail:
<a href="mailto:tobias.kloiber@tum.de">simon.altmannshofer@tum.de</a><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:10.5pt;font-family:Consolas">Internet:
<a href="http://www.rt.mw.tum.de">www.rt.mw.tum.de</a><o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
</div>
</body>
</html>