  The generalized intersection cut (GIC) paradigm is a recent framework for
generating cutting planes in mixed integer programming with attractive
theoretical properties. We investigate this computationally unexplored paradigm
and observe that a key hyperplane activation procedure embedded in it is not
computationally viable. To overcome this issue, we develop a novel replacement
to this procedure called partial hyperplane activation (PHA), introduce a
variant of PHA based on a notion of hyperplane tilting, and prove the validity
of both algorithms. We propose several implementation strategies and parameter
choices for our PHA algorithms and provide supporting theoretical results. We
computationally evaluate these ideas in the COIN-OR framework on MIPLIB
instances. Our findings shed light on the the strengths of the PHA approach as
well as suggest properties related to strong cuts that can be targeted in the
future.
