Zobrazeno 1 - 10
of 127
pro vyhledávání: '"Bergmann, Ronny"'
The classical concept of Fenchel conjugation is tailored to extended real-valued functions defined on linear spaces. In this paper we generalize this concept to functions defined on arbitrary sets that do not necessarily bear any structure at all. Th
Externí odkaz:
http://arxiv.org/abs/2409.04492
We introduce the convex bundle method to solve convex, non-smooth optimization problems on Riemannian manifolds. Each step of our method is based on a model that involves the convex hull of previously collected subgradients, parallely transported int
Externí odkaz:
http://arxiv.org/abs/2402.13670
Autor:
Zimmermann, Ralf, Bergmann, Ronny
In this paper, we propose two methods for multivariate Hermite interpolation of manifold-valued functions. On the one hand, we approach the problem via computing suitable weighted Riemannian barycenters. To satisfy the conditions for Hermite interpol
Externí odkaz:
http://arxiv.org/abs/2212.07281
We propose a novel discrete concept for the total generalized variation (TGV), which has originally been derived to reduce the staircasing effect in classical total variation (TV) regularization, in image denoising problems. We describe discrete, sec
Externí odkaz:
http://arxiv.org/abs/2206.12331
In this paper, we propose a Riemannian version of the difference of convex algorithm (DCA) to solve a minimization problem involving the difference of convex (DC) function. We establish the equivalence between the classical and simplified Riemannian
Externí odkaz:
http://arxiv.org/abs/2112.05250
Publikováno v:
J.Optim.Theory.Appl. 195 (2022) 596-623
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We model the fea
Externí odkaz:
http://arxiv.org/abs/2110.04882
We present the Julia package Manifolds.jl, providing a fast and easy-to-use library of Riemannian manifolds and Lie groups. This package enables working with data defined on a Riemannian manifold, such as the circle, the sphere, symmetric positive de
Externí odkaz:
http://arxiv.org/abs/2106.08777
In this paper, we introduce a definition of Fenchel conjugate and Fenchel biconjugate on Hadamard manifolds based on the tangent bundle. Our definition overcomes the inconvenience that the conjugate depends on the choice of a certain point on the man
Externí odkaz:
http://arxiv.org/abs/2102.11155
Autor:
Baumgärtner, Lukas, Bergmann, Ronny, Herzog, Roland, Schmidt, Stephan, Vidal-Núñez, José, Weiß, Manuel
We present a novel approach to denoising and inpainting problems for surface meshes. The purpose of these problems is to remove noise or fill in missing parts while preserving important features such as sharp edges. A discrete variant of the total va
Externí odkaz:
http://arxiv.org/abs/2012.11748