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% ----- Manopt.jl References -----
% Carefully adapted to BibTeX with Markdown
%
% --- A
%
%
@book{AbsilMahonySepulchre:2008,
AUTHOR = {Absil, P.-A. and Mahony, R. and Sepulchre, R.},
DOI = {10.1515/9781400830244},
NOTE = {available online at \href{https://press.princeton.edu/absil/}{press.princeton.edu/chapters/absil/}},
PUBLISHER = {Princeton University Press},
TITLE = {Optimization Algorithms on Matrix Manifolds},
YEAR = {2008}
}
@article{AbsilBakerGallivan:2006,
DOI = {10.1007/s10208-005-0179-9},
YEAR = {2006},
MONTH = dec,
PUBLISHER = {Springer Science and Business Media LLC},
VOLUME = {7},
NUMBER = {3},
PAGES = {303--330},
AUTHOR = {P.-A. Absil and C.G. Baker and K.A. Gallivan},
TITLE = {Trust-Region Methods on Riemannian Manifolds},
JOURNAL = {Foundations of Computational Mathematics}
}
@article{AdachiOkunoTakeda:2022,
AUTHOR = {Adachi, S. and Okuno, T., and Takeda, A.},
JOURNAL = {ArXiv Preprint},
NUMBER = {2210.00253},
URL = {https://doi.org/10.48550/arXiv.2210.00253},
TITLE = {Riemannian Levenberg-Marquardt Method with Global and Local Convergence Properties},
YEAR = {2022},
}
@article{AgarwalBoumalBullinsCartis:2020,
AUTHOR = {Agarwal, N. and Boumal, N. and Bullins, B. and Cartis, C.},
TITLE = {Adaptive regularization with cubics on manifolds},
JOURNAL = {Mathematical Programming},
PUBLISHER = {Springer Science and Business Media LLC},
YEAR = {2020},
DOI = {10.1007/s10107-020-01505-1}
}
@article{AlmeidaNetoOliveiraSouza:2020,
AUTHOR = {Yldenilson Torres Almeida and João Xavier da Cruz Neto and Paulo Roberto Oliveira and João Carlos de Oliveira Souza},
DOI = {10.1007/s10589-020-00173-3},
JOURNAL = {Computational Optimization and Applications},
MONTH = feb,
NUMBER = {3},
PAGES = {649--673},
PUBLISHER = {Springer Science and Business Media LLC},
TITLE = {A modified proximal point method for {DC} functions on Hadamard manifolds},
VOLUME = {76},
YEAR = {2020},
}
% --- B
%
%
@article{Bacak:2014,
AUTHOR = {Bačák, M.},
DOI = {10.1137/140953393},
JOURNAL = {SIAM Journal on Optimization},
EPRINT = {1210.2145},
EPRINTTYPE = {arXiv},
NUMBER = {3},
PAGES = {1542--1566},
TITLE = {Computing medians and means in Hadamard spaces},
VOLUME = {24},
YEAR = {2014}
}
@article{BacakBergmannSteidlWeinmann:2016,
AUTHOR = {Bačák, Miroslav and Bergmann, Ronny and Steidl, Gabriele and Weinmann, Andreas},
YEAR = {2016},
DOI = {10.1137/15M101988X},
EPRINT = {1506.02409},
EPRINTTYPE = {arXiv},
JOURNAL = {SIAM Journal on Scientific Computing},
NUMBER = {1},
PAGES = {A567--A597},
TITLE = {A second order non-smooth variational model for restoring manifold-valued images},
VOLUME = {38},
}
@inproceedings{Beale:1972,
ADDRESS = {London},
AUTHOR = {Beale, E. M. L.},
BOOKTITLE = {Numerical methods for nonlinear optimization},
EDITOR = {Lootsma, F. A.},
ISBN = {9780124556508},
PAGES = {39–43},
PUBLISHER = {Academic Press, London},
TITLE = {A derivation of conjugate gradients},
YEAR = {1972},
}
@article{Bergmann:2022,
TITLE = {Manopt.Jl: Optimization on Manifolds in Julia},
AUTHOR = {Bergmann, Ronny},
YEAR = {2022},
JOURNAL = {Journal of Open Source Software},
VOLUME = {7},
NUMBER = {70},
PAGES = {3866},
PUBLISHER = {The Open Journal},
DOI = {10.21105/joss.03866}
}
@misc{Bergmann:2022zenodo,
TITLE = {Manopt.Jl},
AUTHOR = {Bergmann, Ronny},
YEAR = {2022},
DOI = {10.5281/zenodo.4290905},
COPYRIGHT = {MIT License},
HOWPUBLISHED = {Zenodo}
}
@article{BergmannFerreiraNemethZhu:2025,
AUTHOR = {Bergmann, R. and Ferreira, O. P. and Németh, S. Z. and Zhu, J.},
JOURNAL = {Preprint, in preparation},
TITLE = {On projection mappings and the gradient projection method
on hyperbolic space forms},
YEAR = {2025}
}
@article{BergmannFerreiraSantosSouza:2024,
AUTHOR = {Bergmann, R. and Ferreira, O. P. and Santos, E. M. and Souza, J. C. O.},
DOI = {10.1007/s10957-024-02392-8},
JOURNAL = {Journal of Optimization Theory and Applications},
TITLE = {The difference of convex algorithm on Hadamard manifolds},
YEAR = {2024},
}
@article{BergmannGousenbourger:2018,
AUTHOR = {Bergmann, Ronny and Gousenbourger, Pierre-Yves},
YEAR = {2018},
EPRINT = {1807.10090},
EPRINTTYPE = {arXiv},
DOI = {10.3389/fams.2018.00059},
JOURNAL = {Frontiers in Applied Mathematics and Statistics},
TITLE = {A variational model for data fitting on manifolds by minimizing the acceleration of a Bézier curve},
VOLUME = {4},
}
@article{BergmannHerzog:2019,
AUTHOR = {Bergmann, Ronny and Herzog, Roland},
DOI = {10.1137/18M1181602},
JOURNAL = {SIAM Journal on Optimization},
EPRINTTYPE = {arXiv},
EPRINT = {1804.06214},
NUMBER = {4},
PAGES = {2423–2444},
TITLE = {Intrinsic formulation of KKT conditions and constraint qualifications on smooth manifolds},
VOLUME = {29},
YEAR = {2019},
}
@article{BergmannHerzogSilvaLouzeiroTenbrinckVidalNunez:2021,
AUTHOR = {Bergmann, Ronny and Herzog, Roland and Silva Louzeiro, Maurício and Tenbrinck, Daniel and Vidal-Núñez, José},
EPRINT = {1908.02022},
EPRINTTYPE = {arXiv},
PUBLISHER = {Springer Science and Business Media LLC},
YEAR = {2021},
MONTH = jan,
DOI = {10.1007/s10208-020-09486-5},
JOURNAL = {Foundations of Computational Mathematics},
NUMBER = {6},
PAGES = {1465--1504},
TITLE = {Fenchel duality theory and a primal-dual algorithm on Riemannian manifolds},
VOLUME = {21},
}
@article{BergmannHerzogJasa:2024,
AUTHOR = {Bergmann, Ronny and Herzog, Roland and Jasa, Hajg},
JOURNAL = {preprint},
EPRINT = {2402.13670},
EPRINTTYPE = {arXiv},
TITLE = {The Riemannian Convex Bundle Method},
YEAR = {2024},
}
@article{BergmannLausSteidlWeinmann:2014:1,
AUTHOR = {Bergmann, Ronny and Laus, Friederike and Steidl, Gabriele and Weinmann, Andreas},
EPRINT = {1405.5349},
EPRINTTYPE = {arXiv},
DOI = {10.1137/140969993},
JOURNAL = {SIAM Journal on Imaging Sciences},
NUMBER = {4},
PAGES = {2916--2953},
TITLE = {Second order differences of cyclic data and applications in variational denoising},
VOLUME = {7},
YEAR = {2014}
}
@article{BergmannPerschSteidl:2016,
AUTHOR = {Bergmann, Ronny and Persch, Johannes and Steidl, Gabriele},
DOI = {10.1137/15M1052858},
EPRINT = {1512.02814},
EPRINTTYPE = {arXiv},
JOURNAL = {SIAM Journal on Imaging Sciences},
NUMBER = {4},
PAGES = {901--937},
TITLE = {A parallel Douglas Rachford algorithm for minimizing ROF-like functionals on images with values in symmetric Hadamard manifolds},
VOLUME = {9},
YEAR = {2016}
}
@article{BergmannJasaJohnPfeffer:2025:1,
AUTHOR = {Bergmann, Ronny and Jasa, Hajg and John, Paula and Pfeffer, Max},
JOURNAL = {preprint},
EPRINT = {2506.09775},
EPRINTTYPE = {arxiv},
TITLE = {The Intrinsic Riemannian Proximal Gradient Method for Nonconvex Optimization},
YEAR = {2025}
}
@article{BergmannJasaJohnPfeffer:2025:2,
AUTHOR = {Bergmann, Ronny and Jasa, Hajg and John, Paula and Pfeffer, Max},
JOURNAL = {preprint},
EPRINT = {2507.16055},
EPRINTTYPE = {arxiv},
TITLE = {The Intrinsic Riemannian Proximal Gradient Method for Convex Optimization},
YEAR = {2025}
}
@book{Bertsekas:2015,
title={Convex Optimization Algorithms},
author={Dimitri P. Bertsekas},
publisher={Athena Scientific},
year={2015},
pages={576},
isbn={978-1886529281},
}
@incollection{BorckmansIshtevaAbsil:2010,
DOI = {10.1007/978-3-642-15461-4_2},
YEAR = {2010},
PUBLISHER = {Springer Berlin Heidelberg},
PAGES = {13--23},
AUTHOR = {Pierre B. Borckmans and Mariya Ishteva and Pierre-Antoine Absil},
TITLE = {A Modified Particle Swarm Optimization Algorithm for the Best Low Multilinear Rank Approximation of Higher-Order Tensors},
BOOKTITLE = {7th International Conference on Swarm INtelligence}
}
@book{Boumal:2023,
TITLE = {An Introduction to Optimization on Smooth Manifolds},
AUTHOR = {Boumal, Nicolas},
YEAR = {2023},
MONTH = mar,
EDITION = {First},
PUBLISHER = {Cambridge University Press},
DOI = {10.1017/9781009166164},
URL = {https://www.nicolasboumal.net/book/index.html},
ABSTRACT = {Optimization on Riemannian manifolds-the result of smooth geometry and optimization merging into one elegant modern framework-spans many areas of science and engineering, including machine learning, computer vision, signal processing, dynamical systems and scientific computing. This text introduces the differential geometry and Riemannian geometry concepts that will help students and researchers in applied mathematics, computer science and engineering gain a firm mathematical grounding to use these tools confidently in their research. Its charts-last approach will prove more intuitive from an optimizer's viewpoint, and all definitions and theorems are motivated to build time-tested optimization algorithms. Starting from first principles, the text goes on to cover current research on topics including worst-case complexity and geodesic convexity. Readers will appreciate the tricks of the trade for conducting research and for numerical implementations sprinkled throughout the book.},
ISBN = {978-1-00-916616-4}
}
@article{ByrdNocedalSchnabel:1994,
title = {Representations of quasi-{Newton} matrices and their use in limited memory methods},
volume = {63},
issn = {1436-4646},
doi = {10.1007/BF01582063},
number = {1},
journal = {Mathematical Programming},
author = {Byrd, Richard H. and Nocedal, Jorge and Schnabel, Robert B.},
month = jan,
year = {1994},
pages = {129--156},
}
@article{ByrdLuNocedalZhu:1995,
title = {A {Limited} {Memory} {Algorithm} for {Bound} {Constrained} {Optimization}},
volume = {16},
issn = {1064-8275},
doi = {10.1137/0916069},
number = {5},
journal = {SIAM Journal on Scientific Computing},
author = {Byrd, Richard H. and Lu, Peihuang and Nocedal, Jorge and Zhu, Ciyou},
month = sep,
year = {1995},
note = {Publisher: Society for Industrial and Applied Mathematics},
pages = {1190--1208},
}
% --- C
%
%
@book{doCarmo:1992,
TITLE = {Riemannian Geometry},
AUTHOR = {do Carmo, Manfredo Perdigão},
YEAR = {1992},
SERIES = {Mathematics: Theory \& Applications},
PAGES = {xiv+300},
PUBLISHER = {Birkhäuser Boston, Inc., Boston, MA},
DOI = {10.1007/978-1-4757-2201-7},
ISBN = {0-8176-3490-8}
}
@techreport{deCasteljau:1959,
AUTHOR = {de Casteljau, Paul},
institution = {Envelope Soleau 40.040, Institute National de la Propriété Industrielle, Paris.},
TITLE = {Outillage methodes calcul},
YEAR = {1959}
}
@techreport{deCasteljau:1963,
AUTHOR = {de Casteljau, Paul},
institution = {Microfiche P 4147-1, Institute National de la Propriété Industrielle, Paris.},
TITLE = {Courbes et surfaces à pôles},
YEAR = {1963}
}
@article{ChambollePock:2011,
AUTHOR = {Chambolle, Antonin and Pock, Thomas},
YEAR = {2011},
DOI = {10.1007/s10851-010-0251-1},
JOURNAL = {Journal of Mathematical Imaging and Vision},
NUMBER = {1},
PAGES = {120--145},
TITLE = {A first-order primal-dual algorithm for convex problems with applications to imaging},
VOLUME = {40}
}
@article{ColuttoFruhaufFuchsScherzer:2010,
title = {The {CMA}-{ES} on {Riemannian} {Manifolds} to {Reconstruct} {Shapes} in 3-{D} {Voxel} {Images}},
volume = {14},
issn = {1941-0026, 1089-778X},
url = {http://ieeexplore.ieee.org/document/5299260/},
doi = {10.1109/TEVC.2009.2029567},
number = {2},
journal = {IEEE Transactions on Evolutionary Computation},
author = {Colutto, S. and Fruhauf, F. and Fuchs, M. and Scherzer, O.},
month = apr,
year = {2010},
pages = {227--245},
}
@book{ConnGouldToint:2000,
DOI = {10.1137/1.9780898719857},
YEAR = {2000},
MONTH = jan,
PUBLISHER = {Society for Industrial and Applied Mathematics},
AUTHOR = {Andrew R. Conn and Nicholas I. M. Gould and Philippe L. Toint},
TITLE = {Trust Region Methods}
}
% ---- D
%
%
@article{DaiYuan:1999,
AUTHOR = {Y. H. Dai and Y. Yuan},
DOI = {10.1137/s1052623497318992},
JOURNAL = {SIAM Journal on Optimization},
MONTH = jan,
NUMBER = {1},
PAGES = {177--182},
PUBLISHER = {Society for Industrial \& Applied Mathematics (SIAM)},
TITLE = {A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property},
VOLUME = {10},
YEAR = {1999}
}
@article{DiepeveenLellmann:2021,
AUTHOR = {Willem Diepeveen and Jan Lellmann},
DOI = {10.1137/21m1398513},
JOURNAL = {SIAM Journal on Imaging Sciences},
MONTH = jan,
EPRINTTYPE = {arXiv},
EPRINT = {2102.10309},
NUMBER = {4},
PAGES = {1565--1600},
PUBLISHER = {Society for Industrial \& Applied Mathematics ({SIAM})},
TITLE = {An Inexact Semismooth Newton Method on Riemannian Manifolds with Application to Duality-Based Total Variation Denoising},
VOLUME = {14},
YEAR = {2021},
}
@article{DoddSharrockNemeth:2024,
title={Learning-rate-free stochastic optimization over Riemannian manifolds},
author={Dodd, Daniel and Sharrock, Louis and Nemeth, Christopher},
journal={arXiv preprint arXiv:2406.02296},
year={2024}
}
@techreport{Dreisigmeyer:2007,
AUTHOR = {Dreisigmeyer, David W.},
INSTITUTION = {Optimization Online},
TITLE = {Direct Search Algorithms over Riemannian Manifolds},
URL = {https://optimization-online.org/?p=9134},
YEAR = {2007}
}
@article{DuranMoelleSbertCremers:2016,
AUTHOR = {Duran, J. and Moeller, M. and Sbert, C. and Cremers, D.},
TITLE = {Collaborative Total Variation: A General Framework for Vectorial TV Models},
JOURNAL = {SIAM Journal on Imaging Sciences},
VOLUME = {9},
NUMBER = {1},
PAGES = {116-151},
YEAR = {2016},
DOI = {10.1137/15M102873X},
EPRINT = {1508.01308},
EPRINTTYPE = {arXiv},
}
% --- E
%
%
@article{El-BakryTapiaTsuchiyaZhang:1996,
AUTHOR = {El-Bakry, A. S. and Tapia, R. A. and Tsuchiya, T. and Zhang, Y.},
DOI = {10.1007/bf02275347},
JOURNAL = {Journal of Optimization Theory and Applications},
NUMBER = {3},
PAGES = {507–541},
TITLE = {On the formulation and theory of the Newton interior-point method for nonlinear programming},
VOLUME = {89},
YEAR = {1996}
}
% --- F
%
%
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