Author

Alberto Del Pia

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Preprint Sep 2026

A quadratic upper bound on the Chv\'atal rank of polytopes in the 0/1-cube

We show that every polytope $P\subseteq[0,1]^n$, and more generally every compact convex set, has Chv\'atal rank at most $12.22n^2+n\log_2 n+2n+4$. This improves the $O(n^2\log n)$ bound of Eisenbrand and Schulz and, together with the $\Omega(n^2)$ lower bound of Rothvo{\ss} and Sanit\`a, shows that the maximum Chv\'at...

Alberto Del Pia · 0 citations

Preprint Sep 2026

Treewidth and the complexity of box-constrained quadratic programs

We consider the problem of minimizing a sparse quadratic function over the unit hypercube. In binary quadratic programming, treewidth of the interaction graph is a central parameter for tractability: bounded treewidth yields polynomial-time solvability. Motivated by this fact, we investigate whether treewidth plays a s...

Alberto Del Pia, Aida Khajavirad · 0 citations