How does GUROBI deal with equality constraints for MIP

[Christoph Neumann]

Hi everyone,

is there a typical way how GUROBI deals with equality constraints on (mixed-)integer variables? E.g. when I have a problem of the form

with some (q,n)-matrix C, (q,m)-matrix D and some q-dimensional vector c, does GUROBI use any elimination procedure to reduce the dimensionality of the problem? 

Cheers,

Christoph

[Tobias Achterberg]

The presolver (more precisely, the aggregator) may decide to remove some of the
variables by substitution (i.e., perform a Gaussian elimination step to get rid
of one variable and one equality constraint).

Moreover, the simplex algorithm solves linear systems all the time and
calculates an LU factorization to do this.

Hope this answers the question.

Regards,

Tobias