Literature
- [ASY+19]
- T. Akiba, S. Sano, T. Yanase, T. Ohta and M. Koyama. Optuna: A Next-generation Hyperparameter Optimization Framework. In: Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2019), arXiv:1907.10902. ↩1
- [ABBR23]
- S. D. Axen, M. Baran, R. Bergmann and K. Rzecki. Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds. ACM Transactions on Mathematical Software (2023), arXiv:2021.08777. ↩1
- [BB26]
- M. Baran and R. Bergmann. A modified Riemannian Levenberg-Marquardt algorithm for robust and constraint optimization on manifolds (2026), arXiv:2606.23560 [math.OC]. ↩1 ↩2 ↩3 ↩4
- [Bac14]
- M. Bačák. Computing medians and means in Hadamard spaces. SIAM Journal on Optimization 24, 1542–1566 (2014), arXiv:1210.2145. ↩1 ↩2 ↩3 ↩4
- [BBSW16]
- [BFNZ25]
- [BFSS24]
- [BFPS17]
- R. Bergmann, J. H. Fitschen, J. Persch and G. Steidl. Infimal convolution coupling of first and second order differences on manifold-valued images. In: Scale Space and Variational Methods in Computer Vision: 6th International Conference, SSVM 2017, Kolding, Denmark, June 4–8, 2017, Proceedings, edited by F. Lauze, Y. Dong and A. B. Dahl (Springer International Publishing, 2017); pp. 447–459. ↩1
- [BFPS18]
- R. Bergmann, J. H. Fitschen, J. Persch and G. Steidl. Priors with coupled first and second order differences for manifold-valued image processing. Journal of Mathematical Imaging and Vision 60, 1459–1481 (2018), arXiv:1709.01343. ↩1
- [BG18]
- R. Bergmann and P.-Y. Gousenbourger. A variational model for data fitting on manifolds by minimizing the acceleration of a Bézier curve. Frontiers in Applied Mathematics and Statistics 4 (2018), arXiv:1807.10090. ↩1 ↩2 ↩3 ↩4 ↩5 ↩6 ↩7
- [BHJ24]
- [BJJP25a]
- [BJJP25b]
- [BLSW14]
- R. Bergmann, F. Laus, G. Steidl and A. Weinmann. Second order differences of cyclic data and applications in variational denoising. SIAM Journal on Imaging Sciences 7, 2916–2953 (2014), arXiv:1405.5349. ↩1 ↩2 ↩3 ↩4 ↩5
- [BPS16]
- R. Bergmann, J. Persch and G. Steidl. A parallel Douglas Rachford algorithm for minimizing ROF-like functionals on images with values in symmetric Hadamard manifolds. SIAM Journal on Imaging Sciences 9, 901–937 (2016), arXiv:1512.02814. ↩1
- [Bou23]
- N. Boumal. An Introduction to Optimization on Smooth Manifolds. First Edition (Cambridge University Press, 2023). ↩1 ↩2 ↩3 ↩4 ↩5
- [Cas59]
- P. de Casteljau. Outillage methodes calcul (Enveloppe Soleau 40.040, Institute National de la Propriété Industrielle, Paris., 1959). ↩1
- [Cas63]
- P. de Casteljau. Courbes et surfaces à pôles (Microfiche P 4147-1, Institute National de la Propriété Industrielle, Paris., 1963). ↩1
- [CMMZ20]
- S. Chen, S. Ma, A. Man-Cho So and T. Zhang. Proximal Gradient Method for Nonsmooth Optimization over the Stiefel Manifold. SIAM Journal on Optimization 30, 210–239 (2020). ↩1 ↩2
- [DMSC16]
- J. Duran, M. Moeller, C. Sbert and D. Cremers. Collaborative Total Variation: A General Framework for Vectorial TV Models. SIAM Journal on Imaging Sciences 9, 116–151 (2016), arXiv:1508.01308. ↩1
- [FO98]
- O. Ferreira and P. R. Oliveira. Subgradient algorithm on Riemannian manifolds. Journal of Optimization Theory and Applications 97, 93–104 (1998). ↩1 ↩2 ↩3
- [Fle13]
- P. T. Fletcher. Geodesic regression and the theory of least squares on Riemannian manifolds. International Journal of Computer Vision 105, 171–185 (2013). ↩1
- [GMS15]
- Y. Gong, D. Meng and E. J. Seibel. Bound constrained bundle adjustment for reliable 3D reconstruction. Optics Express 23, 10771–10785 (2015). ↩1
- [HNP23]
- N. Hoseini Monjezi, S. Nobakhtian and M. R. Pouryayevali. A proximal bundle algorithm for nonsmooth optimization on Riemannian manifolds. IMA Journal of Numerical Analysis 43, 293–325 (2023). ↩1 ↩2 ↩3
- [HW21]
- W. Huang and K. Wei. Riemannian proximal gradient methods. Mathematical Programming 194, 371–413 (2021). ↩1 ↩2
- [JBK+25]
- H. Jasa, R. Bergmann, C. Kümmerle, A. Athreya and Z. Lubberts. Procrustes Problems on Random Matrices, preprint (2025), arXiv:2510.05182. ↩1
- [LNPS17]
- F. Laus, M. Nikolova, J. Persch and G. Steidl. A nonlocal denoising algorithm for manifold-valued images using second order statistics. SIAM Journal on Imaging Sciences 10, 416–448 (2017). ↩1
- [LMS22]
- J. Li, S. Ma and T. Srivastava. A Riemannian ADMM (2022). ↩1 ↩2 ↩3
- [LB19]
- C. Liu and N. Boumal. Simple algorithms for optimization on Riemannian manifolds with constraints. Applied Mathematics & Optimization (2019), arXiv:1091.10000. ↩1 ↩2
- [PN07]
- T. Popiel and L. Noakes. Bézier curves and $C^2$ interpolation in Riemannian manifolds. Journal of Approximation Theory 148, 111–127 (2007). ↩1 ↩2
- [ROF92]
- L. I. Rudin, S. Osher and E. Fatemi. Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60, 259–268 (1992). ↩1
- [SO15]
- J. C. Souza and P. R. Oliveira. A proximal point algorithm for DC fuctions on Hadamard manifolds. Journal of Global Optimization 63, 797–810 (2015). ↩1
- [WS22]
- M. Weber and S. Sra. Riemannian Optimization via Frank-Wolfe Methods. Mathematical Programming 199, 525–556 (2022). ↩1
- [WBS25]
- [WDS14]
- A. Weinmann, L. Demaret and M. Storath. Total variation regularization for manifold-valued data. SIAM Journal on Imaging Sciences 7, 2226–2257 (2014). ↩1 ↩2 ↩3
- [Zac14]
- C. Zach. Robust Bundle Adjustment Revisited. In: Computer Vision – ECCV 2014, Vol. 8693, edited by D. Fleet, T. Pajdla, B. Schiele and T. Tuytelaars (Springer International Publishing, 2014); pp. 772–787. ↩1