Blar i NTNU Open på forfatter "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. (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 Hypergraph p-Laplace for Manifold-valued Data and its Application in Machine-Learning 

      Stokke, Jo Andersson (Master thesis, 2024)
      Grafer og funksjoner på grafer utgjør et omfattende rammeverk for behandling av diskrete data og spiller en stadig viktigere rolle innen mange områder av anvendt matematikk. Grafer gir oss mange verktøy, spesielt graf-Laplace ...

    • The Interior Point Newton Method for Constrained Optimization on Riemannian Manifolds 

      Stokkenes, Markus A. (Master thesis, 2024)
      Indrepunktmetoder er slagkraftige teknikker for å løse storskala ikke-lineære, konvekse, begrensede optimeringsproblemer. I mange optimeringsproblemer oppstående fra den virkelige verden har ikke de underliggende søkerommene ...

    • 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 ...