Consistent Second-Order Conic Integer Programming for Learning Bayesian Networks

Bayesian Networks (BNs) represent conditional probability relations among a set of random variables (nodes) in the form of a directed acyclic graph (DAG), and have found diverse applications in knowledge discovery. We study the problem of learning the sparse DAG structure of a BN from continuous observational data. The central problem can be modeled as … Read more

Low-Complexity Relaxations and Convex Hulls of Disjunctions on the Positive Semidefinite Cone and General Regular Cones

In this paper we analyze general two-term disjunctions on a regular cone $\K$ and derive a general form for a family of convex inequalities which are valid for the resulting nonconvex sets. Under mild technical assumptions, these inequalities collectively describe the closed convex hulls of these disjunctions, and if additional conditions are satisfied, a single … Read more

Disjunctive Cuts for Cross-Sections of the Second-Order Cone

In this paper we provide a unified treatment of general two-term disjunctions on cross-sections of the second-order cone. We derive a closed-form expression for a convex inequality that is valid for such a disjunctive set and show that this inequality is sufficient to characterize the closed convex hull of all two-term disjunctions on ellipsoids and … Read more

Two-Term Disjunctions on the Second-Order Cone

Balas introduced disjunctive cuts in the 1970s for mixed-integer linear programs. Several recent papers have attempted to extend this work to mixed-integer conic programs. In this paper we study the structure of the convex hull of a two-term disjunction applied to the second-order cone, and develop a methodology to derive closed-form expressions for convex inequalities … Read more