Browsing NTNU Open by Author "Bergmann, Ronny"

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    • The Difference of Convex Algorithm on Hadamard Manifolds 

      Bergmann, Ronny; Ferreira, Orizon P.; M. Santos, Elianderson; Souza, João Carlos O. (Preprint, 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 ...

    • 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 ...