In this talk, we present some recent progress on the gap inequalities. In particular:
1. We show how to define gap inequalities for a much more general class of problems (non-convex Mixed-Integer Quadratic Programs).
2. We prove several results concerned with the computational complexity of various problems related to gap inequalities.
3. We present the first ever finite separation algorithm for the gap inequalities.
4. We present some computational results obtained when using gap inequalities as cutting planes.
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