Related papers: Geoopt: Riemannian Optimization in PyTorch
This paper presents the Julia package CCOpt, built on top of the interior-point solver MadNLP. CCOpt implements a suite of algorithms for Mathematical Programs with Complementarity Constraints (MPCCs). The solver additionally comes with…
We introduce geomstats, a python package that performs computations on manifolds such as hyperspheres, hyperbolic spaces, spaces of symmetric positive definite matrices and Lie groups of transformations. We provide efficient and extensively…
Computational optimal transport (OT) offers a principled framework for generative modeling. Neural OT methods, which use neural networks to learn an OT map (or potential) from data in an amortized way, can be evaluated out of sample after…
Riemannian geometry provides the fundamental framework for optimization on nonlinear spaces such as matrix manifolds, which arise in machine learning, signal processing, and robotics. While the underlying theory is classical, existing…
Accurate molecular geometries are a prerequisite for reliable quantum-chemical predictions, yet density functional theory (DFT) optimization remains a major bottleneck for high-throughput molecular screening. Here we present GeoOpt-Net, a…
Conjugate gradient (CG) methods are widely acknowledged as efficient for minimizing continuously differentiable functions in Euclidean spaces. In recent years, various CG methods have been extended to Riemannian manifold optimization, but…
At many scales in neuroscience, appropriate mathematical models take the form of complex dynamical systems. Parametrising such models to conform to the multitude of available experimental constraints is a global nonlinear optimisation…
A novel Python framework for Bayesian optimization known as GPflowOpt is introduced. The package is based on the popular GPflow library for Gaussian processes, leveraging the benefits of TensorFlow including automatic differentiation,…
StructOpt, an open-source structure optimization suite, applies genetic algorithm and particle swarm methods to obtain atomic structures that minimize an objective function. The objective function typically consists of the energy and the…
Machine learning has achieved remarkable success over the past couple of decades, often attributed to a combination of algorithmic innovations and the availability of high-quality data available at scale. However, a third critical component…
The KeOps library provides a fast and memory-efficient GPU support for tensors whose entries are given by a mathematical formula, such as kernel and distance matrices. KeOps alleviates the major bottleneck of tensor-centric libraries for…
Combinatorial optimization problems arise in logistics, scheduling, and resource allocation, yet existing approaches face a fundamental trade-off among generality, performance, and usability. We present cuGenOpt, a GPU-accelerated…
Metaheuristics are widely recognized gradient-free solvers to hard problems that do not meet the rigorous mathematical assumptions of conventional solvers. The automated design of metaheuristic algorithms provides an attractive path to…
Machine-learning-based surrogate models offer significant computational efficiency and faster simulations compared to traditional numerical methods, especially for problems requiring repeated evaluations of partial differential equations.…
Complex Graph Patterns (CGPs), which combine pattern matching with relational operations, are widely used in real-world applications. Existing systems rely on monolithic architectures for CGPs, which restrict their ability to integrate…
In recent years, the quantum computing community has seen an explosion of novel methods to implement non-trivial quantum computations on near-term hardware. An important direction of research has been to decompose an arbitrary entangled…
We present \texttt{MathOptAI.jl}, an open-source Julia library for embedding trained machine learning predictors into a JuMP model. \texttt{MathOptAI.jl} can embed a wide variety of neural networks, decision trees, and Gaussian Processes…
The techniques and analysis presented in this thesis provide new methods to solve optimization problems posed on Riemannian manifolds. These methods are applied to the subspace tracking problem found in adaptive signal processing and…
This paper studies the problem of distributed Riemannian optimization over a network of agents whose cost functions are geodesically smooth but possibly geodesically non-convex. Extending a well-known distributed optimization strategy…
We describe a software package, TomOpt, developed to optimise the geometrical layout and specifications of detectors designed for tomography by scattering of cosmic-ray muons. The software exploits differentiable programming for the…