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.
- [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.
- [Bac14]
- M. Bačák. Computing medians and means in Hadamard spaces. SIAM Journal on Optimization 24, 1542–1566 (2014), arXiv:1210.2145.
- [BBSW16]
- M. Bačák, R. Bergmann, G. Steidl and A. Weinmann. A second order non-smooth variational model for restoring manifold-valued images. SIAM Journal on Scientific Computing 38, A567–A597 (2016), arXiv:1506.02409.
- [BFSS23]
- R. Bergmann, O. P. Ferreira, E. M. Santos and J. C. Souza. The difference of convex algorithm on Hadamard manifolds. Preprint (2023), arXiv:2112.05250.
- [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.
- [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.
- [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.
- [BHJ24]
- R. Bergmann, R. Herzog and H. Jasa. The Riemannian Convex Bundle Method, preprint (2024), arXiv:2402.13670.
- [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.
- [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.
- [Bou23]
- N. Boumal. An Introduction to Optimization on Smooth Manifolds. First Edition (Cambridge University Press, 2023).
- [Cas59]
- P. de Casteljau. Outillage methodes calcul (Enveloppe Soleau 40.040, Institute National de la Propriété Industrielle, Paris., 1959).
- [Cas63]
- P. de Casteljau. Courbes et surfaces à pôles (Microfiche P 4147-1, Institute National de la Propriété Industrielle, Paris., 1963).
- [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.
- [FO98]
- O. Ferreira and P. R. Oliveira. Subgradient algorithm on Riemannian manifolds. Journal of Optimization Theory and Applications 97, 93–104 (1998).
- [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).
- [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).
- [PN07]
- T. Popiel and L. Noakes. Bézier curves and $C^2$ interpolation in Riemannian manifolds. Journal of Approximation Theory 148, 111–127 (2007).
- [ROF92]
- L. I. Rudin, S. Osher and E. Fatemi. Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60, 259–268 (1992).
- [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).
- [WS22]
- M. Weber and S. Sra. Riemannian Optimization via Frank-Wolfe Methods. Mathematical Programming 199, 525–556 (2022).
- [WDS14]
- A. Weinmann, L. Demaret and M. Storath. Total variation regularization for manifold-valued data. SIAM Journal on Imaging Sciences 7, 2226–2257 (2014).