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math.OC2026
Linear Threshold for Oertel's Conjecture on the Mixed-Integer Volume
Hongyu Cheng, Amitabh Basu
Grünbaum's inequality guarantees that the centroid of a convex body has halfspace depth at least : every halfspace containing the centroid captures at least a fraction…
math.OC2026
Theoretical Challenges in Learning for Branch-and-Cut
Hongyu Cheng, Amitabh Basu
Machine learning is increasingly used to guide branch-and-cut (B&C) for mixed-integer linear programming by learning score-based policies for selecting branching variables and cutt…
math.OC2024
Learning Cut Generating Functions for Integer Programming
Hongyu Cheng, Amitabh Basu
The branch-and-cut algorithm is the method of choice to solve large scale integer programming problems in practice. A key ingredient of branch-and-cut is the use of cutting planes…