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<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Hi Dear All:<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>How biggest problems have been tested for IPOPT in terms of
number of design variables and inequality constraints? How efficient is the
IPOPT if the function evaluation and the first-order gradient computation (but
no second-order gradients) are very cheap ( in terms of CPU time on faster Intel
machines). Our goal is to solve two kinds of problems :<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<h2 style='mso-margin-top-alt:0in;margin-right:21.0pt;margin-bottom:0in;
margin-left:32.25pt;margin-bottom:.0001pt;line-height:24.0pt;background:white'><b><font
size=3 face="Times New Roman"><span style='font-size:12.0pt;letter-spacing:
2.4pt;font-weight:normal'>1) about 1-10 millions design variables but a few
number of constraints<o:p></o:p></span></font></b></h2>
<h2 style='mso-margin-top-alt:0in;margin-right:21.0pt;margin-bottom:0in;
margin-left:32.25pt;margin-bottom:.0001pt;line-height:24.0pt;background:white'><b><font
size=3 face="Times New Roman"><span style='font-size:12.0pt;letter-spacing:
2.4pt;font-weight:normal'>2) about 100-50K design variables and 500-100K
constraints<o:p></o:p></span></font></b></h2>
<h2 style='mso-margin-top-alt:0in;margin-right:21.0pt;margin-bottom:0in;
margin-left:32.25pt;margin-bottom:.0001pt;line-height:24.0pt;background:white'><b><font
size=3 face="Times New Roman"><span style='font-size:12.0pt;letter-spacing:
2.4pt;font-weight:normal'><o:p> </o:p></span></font></b></h2>
<h2 style='mso-margin-top-alt:0in;margin-right:21.0pt;margin-bottom:0in;
margin-left:32.25pt;margin-bottom:.0001pt;line-height:24.0pt;background:white'><b><font
size=3 face="Times New Roman"><span style='font-size:12.0pt;letter-spacing:
2.4pt;font-weight:normal'>Another question is if IPOPT use a "active
constraints" concept. Active constraints are the violated or near critical
constraints. The gradients are calculated for active constraints only. Thus, we
can save times for gradient computation (also less memory requirements). In
engineering problems, lots of constraints are inactive.<o:p></o:p></span></font></b></h2>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Thanks,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Xiaoming <o:p></o:p></span></font></p>
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