<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">
<HTML xmlns="http://www.w3.org/TR/REC-html40" xmlns:v =
"urn:schemas-microsoft-com:vml" xmlns:o =
"urn:schemas-microsoft-com:office:office" xmlns:w =
"urn:schemas-microsoft-com:office:word" xmlns:st1 =
"urn:schemas-microsoft-com:office:smarttags"><HEAD>
<META http-equiv=Content-Type content="text/html; charset=iso-8859-1">
<META content="MSHTML 6.00.2900.2963" name=GENERATOR><o:SmartTagType
name="country-region"
namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:SmartTagType><o:SmartTagType
name="City"
namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:SmartTagType><o:SmartTagType
name="PlaceName"
namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:SmartTagType><o:SmartTagType
name="PlaceType"
namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:SmartTagType><o:SmartTagType
name="place"
namespaceuri="urn:schemas-microsoft-com:office:smarttags"></o:SmartTagType><!--[if !mso]>
<STYLE>st1\:* {
BEHAVIOR: url(#default#ieooui)
}
</STYLE>
<![endif]-->
<STYLE>
<!--
/* Font Definitions */
@font-face
{font-family:"MS Mincho";
panose-1:2 2 6 9 4 2 5 8 3 4;}
@font-face
{font-family:"\@MS Mincho";
panose-1:0 0 0 0 0 0 0 0 0 0;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
a:link, span.MsoHyperlink
{color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{color:purple;
text-decoration:underline;}
span.E-MailFormatvorlage17
{mso-style-type:personal;
font-family:Arial;
color:windowtext;}
span.E-MailFormatvorlage18
{mso-style-type:personal-reply;
font-family:Arial;
color:navy;}
@page Section1
{size:595.3pt 841.9pt;
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 vLink=purple link=blue bgColor=#ffffff>
<DIV><FONT size=2>Hi,</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>After years of linear programming, I'm trying my first
QP..</FONT></DIV>
<DIV><FONT size=2>I'm trying to solve the following problem with a quadratic
objective function in CLP:</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>min \sum_i ( z_i * x_i + z_i * y_i )</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>st. </FONT></DIV>
<DIV><FONT size=2> a set of linear constraints,
and</FONT></DIV>
<DIV><FONT size=2> z_i >= 0, x_i >=0, y_i >=
0 for all i</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>I managed to load everything into a ClpModel using a
loadQuadraticObjective with the quad coefficients inserted in a CoinPackedMatrix
called Q.</FONT></DIV>
<DIV><FONT size=2>My problems with solveing this, I think, come from the fact
that Q is not positive semi-definite (it isn't, right?), since this (quadratic
part of the) objective function is _not_ non-negative for all values of the
variables (including infeasible ones like x_i < 0).</FONT></DIV>
<DIV><FONT size=2>My first question is: is this correct? (Sorry for asking
such a basic question..)</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>Let's assume that indeed this is correct and Q is indeed not
positive semi-definite.</FONT></DIV>
<DIV><FONT size=2>My second question then is: but what about the fact that only
for (infeasible) z_i, x_i, y_i < 0 these problems occur? </FONT></DIV>
<DIV><FONT size=2>I was thinking along the lines of maybe providing Clp with a
feasible solution to start with, and then the optimization would work
fine?</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>I'm affraid I'm working horribly outside of my normal area, so
please forgive my possibly ideotic questions..</FONT></DIV>
<DIV><FONT size=2>Any help would be appreciated.</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>Regards,</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2>Jan-Willem Goossens</FONT></DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2></FONT> </DIV>
<DIV><FONT size=2></FONT> </DIV></BODY></HTML>