Students

PhD Students

2022 — 2026

H. Jasa

Algorithms for Nonsmooth Optimization on Riemannian Manifolds, and Applications

PhD thesis Main supervisor. Co-supervisor: B. Owren.

The main focus of this work was the development, convergence analysis, and implementation of methods for optimizing nonsmooth functions that leverage the geometric structure of the problem space. This was done by extending two classical methods for nonsmooth optimization in Euclidean spaces (the bundle method and the proximal gradient method) to the Riemannian setting, and by analyzing and showcasing their performance with several numerical experiments under different assumptions. The algorithms are implemented in the Julia package Manopt.jl, and the numerical experiments in this work are available as notebooks in the package ManoptExamples.jl. The second focus point of this work was the application of the machinery of nonsmooth Riemannian optimization to the Procrustes problem with varying norms. This study justifies the use of a closed-form minimizer as a proxy for the more theoretically rigorous minimizers obtained via nonsmooth Riemannian optimization. While this may seem in contrast with the main focus of the present thesis, these conclusions were enabled precisely by the use of nonsmooth Riemannian optimization. Additionally, this work also serves as a bridge between the fields of Riemannian optimization and statistics, by showcasing an application of methods from the former to a problem from the latter.

2015 — 2018

J. Persch

Optimization Methods in Manifold Valued Image Processing

PhD thesis PI. Main supervisor: G. Steidl.
This work was funded by DFG project BE 5888/2-1.

Supervised Master Theses

Jul 2025

O. G. R. Hovland

Riemannian Optimization applied to Kohn-Sham Density Functional Theory

master thesisM. F. Herbst

Jun 2025

M. A. L. Cid

Intrinsic Newton’s Method for Nonlinear Mappings into Vector Bundles

master thesisA. Schiela, and L. Weigl

Jan 2025

S. E. Oddsen

The Riemannnian LTMADS to solve the Spectral Procrustes problem in Manopt.jl

master thesis The code of this thesis was the basis for the Mesh adaptive direct search solver variant LTMADS, available within Manopt.jl.

Jul 2024

J. A. Stokke

The Hypergraph p-Laplace for Manifold-valued Data and its Application in Machine-Learning

master thesisC. von Tycowicz, and M. Hanik

Jun 2024

M. A. Stokkenes

The Interior Point Newton Method for Constrained Optimization on Riemannian Manifolds

master thesis The code of this thesis was the main basis for The Interior Point Newton Method including its Conjugate Residual sub solver, both available within Manopt.jl.

Jun 2023

V. Lenaerts

Regression of Time Series Data on Manifolds

master thesisD. Huybrechs, and B. Owren This thesis started during an exchange stay and is a master thesis at KU Leuven

Jun 2023

M. R. Munkvold

Adaptive Regularization with Cubics

master thesis The code of this thesis is the Lanczos sub solver variant of and the ARC solver available within Manopt.jl.

Jun 2023

S. Sevland

Multivariate Periodic Wavelets on the Pattern

master thesis

Jun 2023

S. B. Jensen

The nearest $\Omega$-stable matrix via Riemannian Optimization

master thesisR. Zimmermann This thesis was conducted at SDU Odense. Sebastian was staying at NTNU for two weeks to conduct his numerical experiments in Julia.

Sep 2022

R. Dornig

Constraint Optimization on Manifolds

master thesisR. Herzog The code of this thesis was the main basis for The Augmented Lagrangian Method and The Exact Penalty Method available within Manopt.jl.

Jul 2022

E. S. Kjemsås

The Riemannian Frank-Wolfe Algorithm

master thesis The code of this thesis was the basis for The Frank-Wolfe Algorithm available within Manopt.jl.

Jun 2022

J. V. Kolstø

Support Vector Machines on Riemannian Manifolds

master thesis This thesis was awarded the NR Prisen for the best master thesis in mathematics at NTNU within the study year 2021/2022.
Congratulations Johannes!

Jun 2021

M. Weiß

The Chambolle-Pock Algorithm for Geometry Labeling and Segmentation based on the Normal Vector Field

master thesisR. Herzog

Jul 2019

F. Maschke

Geodätische Regression auf Mannigfaltigkeiten mit Nebenbedingungen

master thesisR. Herzog

Sep 2015

M. Löckel

Variational Models and Primal-Dual Algorithms for Manifold-Valued Image Restoration

master thesisG. Steidl

Mar 2015

J. Persch

Analysis of Local Anisotropies and Denoising of $\mathbb S^1$-Valued Data

master thesisG. Steidl

Supervised Bachelor Theses

Jun 2024

J. Stanciewicz

Riemannian center of mass on Kendall's shape space

bachelor thesis

Mar 2022

J.-P. Pfaue

Constrained optimization on Riemannian manifolds using geodesic polygonal sets

bachelor thesisR. Herzog

Dec 2020

T.-C. Riemer

The Riemannian BFGS Method and its Implementation in Julia

bachelor thesisR. Herzog The code is available at within Manopt.jl, see Riemannian quasi Newton Methods.

Nov 2019

R. Dornig

Regularized Clustering of Manifold-Valued Data

bachelor thesisR. Herzog

May 2019

E. Wünsche

$L^1$-TV-Regularisierung von rotationswertigen Daten

bachelor thesisR. Hielscher

Mar 2018

R. Rosandi

Optimization of Composite Bézier Curves on Riemannian Manifolds

bachelor thesis

Mar 2018

J. N. Arf

An Alternating Gradient Descent Method for Geodesic Regression on symmetric Riemannian manifolds

bachelor thesis

Jun 2017

H. Huth

Congruence classes of anisotropic patterns on the torus and application in the FFT-based homogenization

bachelor thesisD. Merkert, B. Simeon, and G. Steidl

May 2017

L. Goebel

Segmentation of Manifold-valued images

bachelor thesisG. Steidl

Jan 2017

B. Schmitt

Anisotropic Structures and Sampling Patterns for the FFT-based Numerical Homogenization

bachelor thesisD. Merkert, B. Simeon, and G. Steidl

Jun 2016

M. Brusius

Unsupervised Co-Segmentation with Histogram Priors

bachelor thesisG. Steidl

Jun 2016

S. J. Neumayer

Entropy Regularized Wasserstein Distances and an Application in Image Segmentation

bachelor thesisG. Steidl

Dec 2013

J. Persch

Directional Information via Structure Tensors

bachelor thesisG. Steidl

Jul 2012

L. Kausch

Multivariate anisotrope Dirichlet-Wavelets zur Kantendetektion auf dem Torus

bachelor thesisJ. Prestin

Oct 2011

I. Hein

Die multivariate periodische Fourier- und Wavelet-Transformation auf anisotropen Mustern

bachelor thesisJ. Prestin

Supervised Specialisation Projects

see TMA4500 Specialization Project, Ind Mat.

Jan 2025

O. G. R. Hovland

Riemannian Optimization using second order Information on the Symplectic Stiefel manifold

specialisation project

Dec 2024

M. A. L. Cid

The Manifold Proximal Gradient Algorithm

specialisation project

Jun 2024

S. E. Oddsen

Derivative-free Optimization on Riemannian Manifolds

specialisation project

Jan 2024

M. A. Stokkenes

Convolutional Neural Network Layers Equivariant Under Affine Lie Group Actions

specialisation project

Oct 2023

J. A. Stokke

Manifold-Valued Graph Learning and Embedding Graphs

specialisation projectC. von Tycowicz, and M. Hanik

Jan 2023

M. R. Munkvold

Low Rank Matrix Completion

specialisation project

Jan 2023

S. Sevland

The Multivariate Fast Fourier Transform on the Pattern

specialisation project

Jan 2022

E. S. Kjemsås

Convolutions on Manifolds for Deep Learning

specialisation project

Jan 2022

J. V. Kolstø

Optimization on the symplectic and the symplectic Stiefel manifold

specialisation project The code is available at within Manifolds.jl, see The symplectic Manifold and the The symplectic Stiefel Manifold.

Supervised Student Projects

Oct 2017

J. N. Arf, and R. Rosandi

Bézier curves in Riemannian manifolds

student project

Oct 2017

J. Settelmeier

Semantic Segmentation using Fully Convolutional Networks

student projectA. Moghiseh

Nov 2016

A. Engel, and L. Goebel

Segmentation of Colour Images Using a Regularised Fuzzy C-Means Algorithm

student project

Sep 2016

H. Huth, and B. Schmitt

Lösung der statischen Wärmeleitungsgleichung in der Homogenisierung auf anisotropen Gittern

student projectD. Merkert

Apr 2016

M. Brusius, and S. J. Neumayer

An Algorithm for Image Segmentation based on Optimal Transport Distances

student projectG. Steidl