Related papers: Partial hyperplane activation for generalized inte…
In mixed-integer programming (MIP) solvers, cutting planes are essential for Branch-and-Cut (B&C) algorithms as they reduce the search space and accelerate the solving process. Traditional methods rely on hard-coded heuristics for cut plane…
The geometric iterative method (GIM) is widely used in data interpolation/fitting, but its slow convergence affects the computational efficiency. Recently, much work was done to guarantee the acceleration of GIM in the literature. In this…
An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the…
Representing large-scale motions and topological changes in the finite volume (FV) framework, while at the same time preserving the accuracy of the numerical solution, is difficult. In this paper, we present a robust, highly efficient…
Cutting planes are a key ingredient to successfully solve mixed-integer linear programs. For specific problems, their strength is often theoretically assessed by showing that they are facet-defining for the corresponding mixed-integer hull.…
Contemporary macro energy systems modelling is characterized by the need to represent strategic and operational decisions with high temporal and spatial resolution and represent discrete investment and retirement decisions. This drive…
Recently, Kronqvist et al.~\cite{KronqvistLundellWesterlund2016} rediscovered the supporting hyperplane algorithm of Veinott~\cite{Veinott1967} and demonstrated its computational benefits for solving convex mixed-integer nonlinear programs.…
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…
The current cut selection algorithm used in mixed-integer programming solvers has remained largely unchanged since its creation. In this paper, we propose a set of new cut scoring measures, cut filtering techniques, and stopping criteria,…
We consider integer programming problems with bounded general-integer variables belonging to the general class of network flow problems. For those, we computationally investigate the effect on mixed-integer linear programming (MIP) solvers…
Solving linear systems of polynomial equations is a ubiquitous problem in both mathematics and physics. The standard approach, Gaussian elimination, scales cubically with system size and often constitutes a computational bottleneck. The…
Deep gradient inversion attacks expose a serious threat to Federated Learning (FL) by accurately recovering private data from shared gradients. However, the state-of-the-art heavily relies on impractical assumptions to access excessive…
We consider the problem of solving a family of parametric mixed-integer linear optimization problems where some entries in the input data change. We introduce the concept of cutting-plane layer (CPL), i.e., a differentiable cutting-plane…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
The design and performance of computer vision algorithms are greatly influenced by the hardware on which they are implemented. CPUs, multi-core CPUs, FPGAs and GPUs have inspired new algorithms and enabled existing ideas to be realized.…
Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous…
In this paper we give a generalization of the well known split cuts of Cook, Kannan and Schrijver to cuts which are based on multi-term disjunctions. They will be called k-disjunctive cuts. The starting point is the question what kind of…
Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…
Graph neural networks (GNNs) are commonly used in semi-supervised settings. Previous research has primarily focused on finding appropriate graph filters (e.g. aggregation methods) to perform well on both homophilic and heterophilic graphs.…
Deep unfolding networks (DUNs) are the foremost methods in the realm of compressed sensing MRI, as they can employ learnable networks to facilitate interpretable forward-inference operators. However, several daunting issues still exist,…