Related papers: Geoopt: Riemannian Optimization in PyTorch
We introduce Riemannian Lyapunov Optimizers (RLOs), a family of optimization algorithms that unifies classic optimizers within one geometric framework. Unlike heuristic improvements to existing optimizers, RLOs are systematically derived…
Manifolds occur naturally as configuration spaces of robotic systems. They provide global descriptions of local coordinate systems that are common tools in expressing positions of robots. The purpose of this survey is threefold. Firstly, we…
We present a homotopic approach to solving challenging, optimization-based motion planning problems. The approach uses Homotopy Optimization, which, unlike standard continuation methods for solving homotopy problems, solves a sequence of…
Gaussian Processes (GPs) are expressive models for capturing signal statistics and expressing prediction uncertainty. As a result, the robotics community has gathered interest in leveraging these methods for inference, planning, and…
The time parallel solution of optimality systems arising in PDE constraint optimization could be achieved by simply applying any time parallel algorithm, such as Parareal, to solve the forward and backward evolution problems arising in the…
Three-dimensional topology optimization (TO) is a powerful technique in engineering design, but readily usable, open-source implementations remain limited within the popular Python scientific environment. This paper introduces PyTopo3D, a…
Data-driven Riemannian geometry has emerged as a powerful tool for interpretable representation learning, offering improved efficiency in downstream tasks. Moving forward, it is crucial to balance cheap manifold mappings with efficient…
In deterministic optimization, it is typically assumed that all problem parameters are fixed and known. In practice, however, some parameters may be a priori unknown but can be estimated from contextual information. A typical…
We describe the optimization algorithm implemented in the open-source derivative-free solver RBFOpt. The algorithm is based on the radial basis function method of Gutmann and the metric stochastic response surface method of Regis and…
PyPOTS is an open-source Python library dedicated to data mining and analysis on multivariate partially-observed time series with missing values. Particularly, it provides easy access to diverse algorithms categorized into five tasks:…
Graphs are ubiquitous, and learning on graphs has become a cornerstone in artificial intelligence and data mining communities. Unlike pixel grids in images or sequential structures in language, graphs exhibit a typical non-Euclidean…
We introduce Geometric Neural Operators (GNPs) for accounting for geometric contributions in data-driven deep learning of operators. We show how GNPs can be used (i) to estimate geometric properties, such as the metric and curvatures, (ii)…
In this article, we propose a Newton-based method for solving multiobjective interval optimization problems (MIOPs). We first provide a connection between weakly Pareto optimal points and Pareto critical points in the context of MIOPs.…
SOSOPT is a Matlab toolbox for formulating and solving Sum-of-Squares (SOS) polynomial optimizations. This document briefly describes the use and functionality of this toolbox. Section 1 introduces the problem formulations for SOS tests,…
Nonlinear Parametric Optimization Network (NLPOpt-Net) is an unsupervised learning architecture to solve constrained nonlinear programs (NLP). Given the structure of an NLP, it learns the parametric solution maps with guaranteed constraint…
Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…
In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue…
We examine popular gradient-based algorithms for nonlinear control in the light of the modern complexity analysis of first-order optimization algorithms. The examination reveals that the complexity bounds can be clearly stated in terms of…
Optimization problems on the generalized Stiefel manifold (and products of it) are prevalent across science and engineering. For example, in computational science they arise in symmetric (generalized) eigenvalue problems, in nonlinear…
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…