Detailed Description

aggregate variables by dual arguments

Author: Dieter Weninger

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 , constraint c can only be fulfilled for , and
if , constraint c becomes redundant and can be dual-fixed to its upper bound (or vice versa). Then we can perform the following aggregation: .