Manopt, a Matlab toolbox for optimization on manifolds. Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus is on problems where the smooth geometry of the search space can be leveraged to design efficient numerical algorithms. In particular, optimization on manifolds is well-suited to deal with rank and orthogonality constraints. Such structured constraints appear pervasively in machine learning applications, including low-rank matrix completion, sensor network localization, camera network registration, independent component analysis, metric learning, dimensionality reduction and so on. The Manopt toolbox, available at , is a user-friendly, documented piece of software dedicated to simplify experimenting with state of the art Riemannian optimization algorithms. We aim particularly at reaching practitioners outside our field

References in zbMATH (referenced in 106 articles , 1 standard article )

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  1. Agarwal, Naman; Boumal, Nicolas; Bullins, Brian; Cartis, Coralia: Adaptive regularization with cubics on manifolds (2021)
  2. Breiding, Paul; Vannieuwenhoven, Nick: The condition number of Riemannian approximation problems (2021)
  3. Dong, Shuyu; Absil, P.-A.; Gallivan, K. A.: Riemannian gradient descent methods for graph-regularized matrix completion (2021)
  4. Dong, Yuexiao: A brief review of linear sufficient dimension reduction through optimization (2021)
  5. Francisco, Juliano B.; Gonçalves, Douglas Soares; Viloche Bazán, Fermín S.; Paredes, Lila L. T.: Nonmonotone inexact restoration approach for minimization with orthogonality constraints (2021)
  6. Gao, Bin; Son, Nguyen Thanh; Absil, P.-A.; Stykel, Tatjana: Riemannian optimization on the symplectic Stiefel manifold (2021)
  7. Krumnow, Christian; Pfeffer, Max; Uschmajew, André: Computing eigenspaces with low rank constraints (2021)
  8. Li, Jiao-fen; Li, Wen; Duan, Xue-feng; Xiao, Mingqing: Newton’s method for the parameterized generalized eigenvalue problem with nonsquare matrix pencils (2021)
  9. Li, Ji; Cai, Jian-Feng; Zhao, Hongkai: Scalable incremental nonconvex optimization approach for phase retrieval (2021)
  10. Li, Xiaobo; Wang, Xianfu; Krishan Lal, Manish: A nonmonotone trust region method for unconstrained optimization problems on Riemannian manifolds (2021)
  11. Seth D. Axen, Mateusz Baran, Ronny Bergmann, Krzysztof Rzecki: Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds (2021) arXiv
  12. Sutti, Marco; Vandereycken, Bart: Riemannian multigrid line search for low-rank problems (2021)
  13. Won, Joong-Ho; Zhou, Hua; Lange, Kenneth: Orthogonal trace-sum maximization: applications, local algorithms, and global optimality (2021)
  14. Wu, Runxiong; Chen, Xin: MM algorithms for distance covariance based sufficient dimension reduction and sufficient variable selection (2021)
  15. Yao, Teng-Teng; Zhao, Zhi; Bai, Zheng-Jian; Jin, Xiao-Qing: A Riemannian derivative-free Polak-Ribiére-Polyak method for tangent vector field (2021)
  16. Yurtsever, Alp; Tropp, Joel A.; Fercoq, Olivier; Udell, Madeleine; Cevher, Volkan: Scalable semidefinite programming (2021)
  17. Almeida, Yldenilson Torres; da Cruz Neto, João Xavier; Oliveira, Paulo Roberto; de Oliveira Souza, João Carlos: A modified proximal point method for DC functions on Hadamard manifolds (2020)
  18. Bendory, Tamir; Edidin, Dan; Eldar, Yonina C.: On signal reconstruction from FROG measurements (2020)
  19. Bortoloti, Marcio Antônio de A.; Fernandes, Teles A.; Ferreira, Orizon P.; Yuan, Jinyun: Damped Newton’s method on Riemannian manifolds (2020)
  20. Bouchard, Florent; Afsari, Bijan; Malick, Jérôme; Congedo, Marco: Approximate joint diagonalization with Riemannian optimization on the general linear group (2020)

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