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<p>Dear Amir,</p>
<p>in a branch-and-price algorithm, you solve every node LP via
column generation. At the end of that process, the current LP
solution provides a valid lower bound. This is what SCIP installs
as lower bound of the node, and if you call SCIPgetDualBound after
the root LP finished solving with column generation (and before
the branch-and-bound continued), you will get this bound.</p>
<p>Of course, there are other means to compute valid lower bound,
e.g., the Lagrangian dual bound if you solved all pricing problems
to optimality in one pricing round and know an upper bound on the
sum of solution values for all variables of a pricing problem in
each LP solution. This cannot be done automatically, because you
implement the pricer yourself, however, if you can compute such a
bound, you can pass it to SCIP via the lowerbound pointer given to
the pricing callback.</p>
<p>Best,<br>
Gerald<br>
</p>
<br>
<div class="moz-cite-prefix">On 13.09.2017 21:24, Amir Mansouri
wrote:<br>
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<p class="MsoNormal">Hi SCIPers,<span dir="RTL"
style="font-family:"Arial",sans-serif"
lang="AR-SA"><o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I am solving an integer problem using a
branch and price algorithm. <o:p></o:p></p>
<p class="MsoNormal">I need to have a global lower bound for my
problem.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Note that all columns are not included in
the root node. So the linear programming relaxation does not
work here.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Does scipgetdualbound in the root node
provide a lower bound for my problem?<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">If it does, could you provide me with
detail of computing the lower bound?<o:p></o:p></p>
<p class="MsoNormal">Which theorem or inequality is used to get
the lower bound?<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">If it does not, how can I get a lower
bound?<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Thanks,<o:p></o:p></p>
<p class="MsoNormal">Amir<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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