95 citations · 482 across the 27 of their papers we have counts for
4 papers · 1 filter
The difference of convex algorithm on Hadamard manifolds
Ronny Bergmann, Orizon P. Ferreira, Elianderson M. Santos +1
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 esta…
First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints
Ronny Bergmann, Roland Herzog, Julián Ortiz López +1
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 cod…
Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds
Seth D. Axen, Mateusz Baran, Ronny Bergmann +1
We present the Julia package Manifoldsjl, providing a fast and easy-to-use library of Riemannian manifolds and Lie groups. This package enables working with data defined on a Ri…
Fenchel Duality and a Separation Theorem on Hadamard Manifolds
Maurício Silva Louzeiro, Ronny Bergmann, Roland Herzog
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…