Blar i NTNU Open på forfatter "Bergmann, Ronny"
-
The Difference of Convex Algorithm on Hadamard Manifolds
Bergmann, Ronny; Ferreira, Orizon P.; M. Santos, Elianderson; Souza, João Carlos O. (Journal article, 2024)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. The equivalence between the classical and simplified ... -
Fenchel Duality and a Separation Theorem on Hadamard Manifolds
Silva Louzeiro, Maurício; Bergmann, Ronny; Herzog, Roland (Peer reviewed; Journal article, 2022)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 ... -
First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints
Bergmann, Ronny; Herzog, Roland; Ortiz López, Julian; Schiela, Anton (Peer reviewed; Journal article, 2022)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.jl: An Extensible Julia Framework for Data Analysis on Manifolds
Axen, Seth D.; Baran, Mateusz; Bergmann, Ronny; Rzecki, Krzysztof (Peer reviewed; Journal article, 2023)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 ... -
Manopt.jl: Optimization on Manifolds in Julia
Bergmann, Ronny (Journal article; Peer reviewed, 2022)Manopt.jl provides a set of optimization algorithms for optimization problems given on a Riemannian manifold M. Based on a generic optimization framework, together with the interface ManifoldsBase.jl for Riemannian manifolds, ... -
Multivariate Hermite interpolation of manifold-valued data
Zimmermann, Ralf; Bergmann, Ronny (Journal article, 2024)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 ... -
Multivariate Periodic Wavelets on the Pattern
Sevland, Solvor (Master thesis, 2023)I denne masteren analyserer me bilete og oppdagar kantar ved hjelp av fleirdimensjonale periodiske wavelets og fleirskala-analyse, på engelsk multiresolusion analysis. Me presanterer kongruensklassa til det $d$-variate ... -
Riemannian center of mass on Kendall's shape space
Stankiewicz, Jacek (Bachelor thesis, 2024)I denne teksten har vi gitt en innføring i teorien for mangfoldigheter. Denne teorien ble utviklet i forbindelse med optimalisering på mangfoldigheter. Funksjonen vi optimaliserte, var funksjonen som definerte det riemannske ... -
Support Vector Machines on Riemannian Manifolds
Kolstø, Johannes Voll (Master thesis, 2022)Støttevektormaskiner er nyttige verktøy brukt til binærklassifikasjon av datasett på Hilbertrom. I noen applikasjoner derimot, slik som å klassifisere hippocampuser til mennesker med schizofreni eller separare hjernesignaler ... -
The Riemannian Frank–Wolfe Algorithm
Kjemsås, Even Stephansen (Master thesis, 2022)Frank–Wolfe-algoritmen er en iterativ optimeringsalgoritme for å løse betingede optimeringsproblemer. Metoden er basert på å forenkle problemet til et lineært delproblem som løses i hver iterasjon, og fungerer spesielt bra ... -
Variation for Piecewise Constant Functions on Triangular Meshes with Applications in Imaging
Baumgartner, Lukas; Bergmann, Ronny; Herzog, Roland; Schmidt, Stephan; Vidal Núñez, José (Journal article, 2023)We propose a novel discrete concept for the total generalized variation (TGV), which was originally derived to reduce the staircasing effect in classical total variation regularization, in image denoising problems. We ...