Related papers: Learning Cuts via Enumeration Oracles

We study a mixed integer linear program with m integer variables and k non-negative continuous variables in the form of the relaxation of the corner polyhedron that was introduced by Andersen, Louveaux, Weismantel and Wolsey [Inequalities…

We consider so-called squaring the square-puzzles where a given square (or rectangle) should be dissected into smaller squares. For a specific instance of such problems we demonstrate that a mathematically rigorous solution can be quite…

We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…

In this workshop, we discuss several algorithms for mathematical programs with equilibrium constraints (MPECs). The unifying theme is that MPECs are optimization problems whose feasible set contains a lower-level equilibrium system, often…

Deep learning has received much attention lately due to the impressive empirical performance achieved by training algorithms. Consequently, a need for a better theoretical understanding of these problems has become more evident in recent…

Floor planning is an important and difficult task in architecture. When planning office buildings, rooms that belong to the same organisational unit should be placed close to each other. This leads to the following NP-hard mathematical…

Starting from a classic financial optimization problem, we first propose a cutting plane algorithm for this problem. Then we use spectral decomposition to tranform the problem into an equivalent D.C. programming problem, and the…

Smoothed online learning has emerged as a popular framework to mitigate the substantial loss in statistical and computational complexity that arises when one moves from classical to adversarial learning. Unfortunately, for some spaces, it…

Ensemble learning combines multiple classifiers in the hope of obtaining better predictive performance. Empirical studies have shown that ensemble pruning, that is, choosing an appropriate subset of the available classifiers, can lead to…

Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…

Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…

Classifying orthogonal arrays is a well known important class of problems that asks for finding all non-isomorphic, non-negative integer solutions to a class of systems of constraints. Solved instances are scarce. We develop two new methods…

We present a novel AI-assisted method for decomposing (segmenting) planar CAD (computer-aided design) models into well shaped rectangular blocks as a proof-of-principle of a general decomposition method applicable to complex 2D and 3D CAD…

One of the most effective algorithms for differentially private learning and optimization is objective perturbation. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and…

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 cutting planes. Many approaches train on local signals from…

We show that the model of quantum computation based on density matrices and superoperators can be decomposed in a pure classical (functional) part and an effectful part modeling probabilities and measurement. The effectful part can be…

Second-order methods are of great importance for composite convex optimization problems due to their local super-linear convergence rates (under appropriate assumptions). However, the presence of even a simple nonsmooth function in the…

We study to what extent quantum algorithms can speed up solving convex optimization problems. Following the classical literature we assume access to a convex set via various oracles, and we examine the efficiency of reductions between the…

In this paper we present a new algorithm for learning oblique decision trees. Most of the current decision tree algorithms rely on impurity measures to assess the goodness of hyperplanes at each node while learning a decision tree in a…

Mixed-integer nonlinear optimization encompasses a broad class of problems that present both theoretical and computational challenges. We propose a new type of method to solve these problems based on a branch-and-bound algorithm with convex…