Amitabh Basu

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20242026

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math.MG2026

A centerpoint theorem for three planar convex bodies

Hongyu Cheng, Amitabh Basu

For planar convex bodies $A_{0}, A_{1}, A_{2}$ satisfying $\frac{1}{2} (A_{0} + A_{2}) \subseteq A_{1}$ , we prove that the union of the three slices ${i} \times A_{i} \subseteq R^{3}$ , $i = 0, 1, 2$ , co…

cs.LG2026

Sample Complexity of Stochastic Optimization with Integer Variables

Hongyu Cheng, Yinghao Zheng, Marco Molinaro +1

We establish sample complexity results for stochastic optimization over the integers, especially with a view to understand the complexity with respect to the corresponding continuo…

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 $1/ e$ : every halfspace containing the centroid captures at least a $1/ e$ fraction o…

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…