aggregate variables by dual arguments
This presolver looks for variables which could not be handled by duality fixing because of one up-/downlock. If the constraint which delivers the up-/downlock has a specific structure, we can aggregate the corresponding variable.
In more detail (for a minimization problem and the case of only one uplock):
Given a variable \(x_i\) with \(c_i \leq 0\) and only one up lock (originating from a constraint c), we are looking for a binary variable \(x_j\) such that:
- if \(x_j = 0\), constraint c can only be fulfilled for \(x_i = lb_i\), and
- if \(x_j = 1\), constraint c becomes redundant and \(x_i\) can be dual-fixed to its upper bound \(ub_i\) (or vice versa). Then we can perform the following aggregation: \(x_i = lb_i + x_j (ub_i - lb_i)\).
Similar arguments apply for the case of only one down lock and \(c_i \geq 0\).
Definition in file presol_dualagg.h.
|SCIP_EXPORT SCIP_RETCODE||SCIPincludePresolDualagg (SCIP *scip)|