Binary bilevel programs are challenging to solve due to the lack of compact single-level reformulations. Recent extended network flow-based reformulations have emerged as a promising approach, providing strong dual bounds. However, their increasing size can make them computationally prohibitive. We develop a cutting-plane framework that exploits these networks without requiring an extended-space formulation. We introduce … Read more
Distributionally robust optimization hedges a decision against an ambiguity set of candidate distributions. In a cold-start setting the target distribution is unobserved and no sample from it is available, so only related source distributions provide evidence for constructing that set. We propose an inclusive-exclusive Wasserstein ball model that jointly learns a center and radius from … Read more
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\’atal rank of a polytope in $[0,1]^n$ is $\Theta(n^2)$. More … Read more
We study the steady-state expansion problem for potential-based flow networks. Constructing a cost-minimal network that admits a flow satisfying the underlying physical laws is a central problem in the design of gas, hydrogen, water, and electricity infrastructures. The physical behavior of such networks is governed by nonlinear relations between arc flows and the potential differences … Read more
Decision diagrams (DDs) have become a powerful tool for discrete optimization, supporting a wide range of algorithms that span cut-generation procedures, decomposition methods, and specialized branch-and-bound searches. Despite this growth, their adoption remains limited, partly because most existing DD code is tailored to a specific algorithm or application and is therefore hard to reuse. We … Read more
We study cutting-plane generation for binary polynomial optimization (BPO), whose feasible region is the multilinear set of a hypergraph. Strong inequalities for this set—such as two-links, flowers, and odd $\beta$-cycles—are classically hand-derived for fixed support patterns. Instead, we propose a decision-diagram (DD) approach: for any chosen support, it separates a facet-defining cut in the local … Read more
Minimum distance constraints (minDCs) appear in many geometric optimization problems. They pose major challenges for mixed-integer nonlinear programming (MINLP) due to their reverse-convexity. We develop new algorithms for tightening variable bounds in general MINLPs with minDCs. Because many such problems exhibit substantial symmetry, we further discuss an approach for handling rotation symmetries. In a computational … Read more
We present an exact method for separating Chvátal-Gomory cuts from binary knapsack sets, consisting of two steps: i) enumerating a finite set of possible optimal multipliers for the knapsack constraint; ii) for each candidate, adjusting optimally the remaining multipliers. We prove that ii) can be formulated as a binary knapsack problem, leading to a pseudopolynomial-time … Read more
Over the last decades, using piecewise-linear mixed-integer relaxations of nonlinear expressions has become a strong alternative to spatial branching for solving mixed-integer nonlinear programs. Since these relaxations give rise to large numbers of binary variables that encode interval selections, strengthening them is crucial. We investigate how to exploit the resulting combinatorial structure by integrating cutting-plane … Read more
The cone of positive semi-definite (SDP) matrices can be described by an infinite number of linear constraints. It is well-known that one can optimize over such a feasible area by standard Cutting Planes, but work on this idea remains a rare sight, likely due to its limited practical appeal compared to Interior Point Methods (IPMs). … Read more