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• Gurobi Staff

Hello Yannic:

barHomogeneous = 1 parameter refers to using the so-called homogeneous self-dual embedding that amongst other things allows to set the initial point for the barrier (the other alternative is the so-called infeasible start IPM).  You can find some background here, https://pubsonline.informs.org/doi/10.1287/moor.19.1.53 and there are many other papers on the subject (LP is not very difficult to extend to SOCP).

We typically see the homogeneous embedding as more numerically stable but a little bit more expensive computationally, so it is not used as the default setting.

Hope this helps.