Tong Xu The integer quadratic moment hull is the closed convex hull of the pairs \((z,zz^{\top})\) with \(z\in\mathbb{Z}^n\). We prove that one round of Chvátal–Gomory (CG) cuts applied to its basic semidefinite relaxation recovers this hull exactly if and only if \(n\le6\). Our approach identifies its facets with perfect Delaunay polyhedra and characterizes their recovery through depth, … Read more
We consider mixed-integer convex optimization problems in which binary indicators control continuous variables. We introduce the Coordinate Optimality Reformulation (CORe) framework, which augments standard indicator formulations by incorporating coordinate-wise optimality information. The resulting reformulations preserve global optimality while substantially improving branch-and-bound performance, particularly in sparse and structured settings where the coordinate-wise optimality conditions expose exploitable … Read more
This paper studies the problem of learning Bayesian networks from continuous observational data, generated according to a linear Gaussian structural equation model. We consider an \(\ell_0\)-penalized maximum likelihood estimator for this problem which is known to have favorable statistical properties but is computationally challenging to solve, especially for medium-sized Bayesian networks. We propose a new … Read more