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<font face="monospace">Dear Alexander,<br>
<br>
I assume that in your problem description you are using the LP
format. However, the documentation<br>
<br>
<a class="moz-txt-link-freetext" href="https://www.tu-chemnitz.de/mathematik/discrete/manuals/cplex/doc/refman/html/appendixE5.html">https://www.tu-chemnitz.de/mathematik/discrete/manuals/cplex/doc/refman/html/appendixE5.html</a><br>
<br>
states "... <, <=, =<, >, >=, =>, and =. These
are interpreted as <=, <=, <=, >=, >=, >= and =,
respectively". The reason is that linear programs (which are used
as relaxations for IPs) in general do not allow strict
inequalities.<br>
<br>
Best,<br>
Matthias<br>
</font><br>
<div class="moz-cite-prefix">On 03.03.22 01:17, Alex Meiburg wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CACs9yV81ZhTEKexVEfiZsNwb9txHXqM_THtXGwO=Sjs52SwXWg@mail.gmail.com">
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<div>I noticed that SCIP doesn't seem to like strict
inequalities for integers. When it solves</div>
<div><br>
</div>
<div>Maximize<br>
k<br>
st<br>
k < 10<br>
Integer<br>
k</div>
<div><br>
</div>
<div>I get the solution</div>
<div><br>
</div>
<div>solution status: optimal solution found<br>
objective value: 10<br>
k 10 (obj:1)</div>
<div><br>
</div>
<div>When of course that's not actually feasible. :) In this
case of course it's pretty simple to remedy by replacing
"[foo] < N" by "[foo] <= N-1". But that's not always
valid, e.g. in the problem</div>
<div><br>
</div>
<div>Maximize<br>
halfK<br>
st<br>
</div>
<div>halfK < 10</div>
<div>halfK + halfK = k<br>
</div>
<div>Integer<br>
k</div>
<div><br>
</div>
<div>... in which case the correct answer is 9.5 (and SCIP think
it's 10). I'm using SCIP v7.0.2. Is there any interest in
fixing this, or at least, documenting it better...? I skimmed
and couldn't find any warnings about not using strict
inequalities.<br>
</div>
<div><br>
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<div>
<div dir="ltr" class="gmail_signature"
data-smartmail="gmail_signature">
<div dir="ltr">-- Alexander Meiburg<br>
</div>
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<br>
<fieldset class="moz-mime-attachment-header"></fieldset>
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