<html>
<head>
<meta content="text/html; charset=ISO-8859-1"
http-equiv="Content-Type">
</head>
<body text="#000000" bgcolor="#FFFFFF">
<div class="moz-cite-prefix">Dear Abdelkader Ouali,<br>
<br>
welcome to the SCIP mailing list. <br>
SCIP only accepts linear objective functions as input, every
nonlinear (or in your case piecewise linear) objective <br>
has to be modeled via additional constraints.<br>
<br>
The first attempt I would do in your situation is a linearization
of all <br>
|f_i x_i - f_j x_j| by adding two continuous variables y⁺_{ij}
>= 0, y⁻_{ij} >= 0 and a constraint<br>
f_i x_i - f_j x_j = y⁺_{ij} - y⁻_{ij}. Then replace your objective
function by \sum \sum y⁺_{ij} + y⁻_{ij}, and <br>
you obtain the desired result.<br>
<br>
Best regards,<br>
Gregor<br>
<br>
<br>
<br>
Am 06.06.2014 11:34, schrieb Abdelkader Ouali:<br>
</div>
<blockquote cite="mid:DUB129-W60AFC04338237E07B9FBC3AB2C0@phx.gbl"
type="cite">
<style><!--
.hmmessage P
{
margin:0px;
padding:0px
}
body.hmmessage
{
font-size: 12pt;
font-family:Calibri
}
--></style>
<div dir="ltr">Dear Scip users,
<div><br>
</div>
<div>I'am newer in SCIP solver, i know the basic steps to model
and solve MIP</div>
<div>using cpp wrapper for column generation.</div>
<div><br>
</div>
<div>My question concern the objective function in SCIP. When
adding variables to the problem.</div>
<div>In the original problem, <span style="font-size: 12pt;">each
time we use SCIPaddVar(),</span><span style="font-size:
12pt;"> </span><span style="font-size: 12pt;"> SCIP
construct the objective as </span></div>
<div><span style="font-size: 12pt;">follow (notation in latex
format) </span><span style="font-size: 12pt;">:</span></div>
<div><br>
</div>
<div><b style="font-size: 12pt;"><span style="color: rgb(128, 0,
0);">\min</span> z = </b><b><span style="font-size:
12pt; color: rgb(128, 0, 0);">\sum</span><span
style="font-size: 12pt;">{i </span><span
style="font-size: 12pt; color: rgb(128, 0, 0);">\in</span><span
style="font-size: 12pt;"> </span><span style="font-size:
12pt;">vars</span><span style="font-size: 12pt;">} </span><span
style="font-size: 12pt;">C_i</span><span style="font-size:
12pt;"> </span><span style="font-size: 12pt;">vars_i</span></b>,
where <b>C_i</b> is the objective of variable, and <b>vars_i</b>
its associated variable.</div>
<div><br>
</div>
<div>In my case, i don't want to use this formula to construct
my objective function. To be more clear,</div>
<div>my objective function has the form :</div>
<div><br>
</div>
<div>
<pre style="margin-top: 0px; margin-bottom: 0px;"><b><span style="font-family: Calibri, sans-serif; font-size: 12pt; color: rgb(128, 0, 0);">\min</span><span style="font-family: Calibri, sans-serif; font-size: 12pt;"> z= </span><span style="font-family: Calibri, sans-serif; font-size: 12pt; color: rgb(128, 0, 0);">\sum_</span><span style="font-family: Calibri, sans-serif; font-size: 12pt;">{I </span><span style="font-family: Calibri, sans-serif; font-size: 12pt; color: rgb(128, 0, 0);">\in</span><span style="font-family: Calibri, sans-serif; font-size: 12pt;"> X} </span><span style="font-family: Calibri, sans-serif; font-size: 12pt; color: rgb(128, 0, 0);">\sum_</span><span style="font-family: Calibri, sans-serif; font-size: 12pt;">{J </span><span style="font-family: Calibri, sans-serif; font-size: 12pt; color: rgb(128, 0, 0);">\in</span><span style="font-family: Calibri, sans-serif; font-size: 12pt;"> X} </span><span style="font-family: Calibri, sans-serif; font-!
size: 12pt
;">|f_I</span><span style="font-family: Calibri, sans-serif; font-size: 12pt;"> </span><span style="font-family: Calibri, sans-serif; font-size: 12pt;">X_I</span><span style="font-family: Calibri, sans-serif; font-size: 12pt;"> - </span><span style="font-family: Calibri, sans-serif; font-size: 12pt;">f_J</span><span style="font-family: Calibri, sans-serif; font-size: 12pt;"> </span><span style="font-family: Calibri, sans-serif; font-size: 12pt;">X_J|</span></b>,<font face="Calibri"> <font size="4">where X is set of boolean variables, f_I<!--EndFragment--></font></font></pre>
<pre style="margin-top: 0px; margin-bottom: 0px;"><font size="4" face="Calibri">their associated objective values.</font></pre>
<pre style="margin-top: 0px; margin-bottom: 0px;">
</pre>
<pre style="margin-top: 0px; margin-bottom: 0px;"><font size="4" face="Calibri">I want to know if there some c++ SCIP functions, that allow me, to express my objective function</font></pre>
<pre style="margin-top: 0px; margin-bottom: 0px;"><font size="4"><font face="Calibri">as i want ?</font></font></pre>
<pre style="margin-top: 0px; margin-bottom: 0px;"><font size="4">
</font></pre>
<pre style="margin-top: 0px; margin-bottom: 0px;"><font size="4"><font face="Calibri">Thank you for any response or documentations about this question</font></font></pre>
<pre style="margin-top: 0px; margin-bottom: 0px;"><font size="4">
</font></pre>
<pre style="margin-top: 0px; margin-bottom: 0px;"><font size="4">---</font></pre>
<pre style="margin-top: 0px; margin-bottom: 0px;"><font size="4">Abdelkader Ouali </font></pre>
</div>
</div>
<br>
<fieldset class="mimeAttachmentHeader"></fieldset>
<br>
<pre wrap="">_______________________________________________
Scip mailing list
<a class="moz-txt-link-abbreviated" href="mailto:Scip@zib.de">Scip@zib.de</a>
<a class="moz-txt-link-freetext" href="http://listserv.zib.de/mailman/listinfo/scip">http://listserv.zib.de/mailman/listinfo/scip</a>
</pre>
</blockquote>
<br>
</body>
</html>