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 97 articles , 1 standard article )

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  1. Breiding, Paul; Vannieuwenhoven, Nick: The condition number of Riemannian approximation problems (2021)
  2. Dong, Yuexiao: A brief review of linear sufficient dimension reduction through optimization (2021)
  3. Francisco, Juliano B.; Gonçalves, Douglas Soares; Viloche Bazán, Fermín S.; Paredes, Lila L. T.: Nonmonotone inexact restoration approach for minimization with orthogonality constraints (2021)
  4. Krumnow, Christian; Pfeffer, Max; Uschmajew, André: Computing eigenspaces with low rank constraints (2021)
  5. Li, Ji; Cai, Jian-Feng; Zhao, Hongkai: Scalable incremental nonconvex optimization approach for phase retrieval (2021)
  6. Wu, Runxiong; Chen, Xin: MM algorithms for distance covariance based sufficient dimension reduction and sufficient variable selection (2021)
  7. Yao, Teng-Teng; Zhao, Zhi; Bai, Zheng-Jian; Jin, Xiao-Qing: A Riemannian derivative-free Polak-Ribiére-Polyak method for tangent vector field (2021)
  8. 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)
  9. Bendory, Tamir; Edidin, Dan; Eldar, Yonina C.: On signal reconstruction from FROG measurements (2020)
  10. Bortoloti, Marcio Antônio de A.; Fernandes, Teles A.; Ferreira, Orizon P.; Yuan, Jinyun: Damped Newton’s method on Riemannian manifolds (2020)
  11. Bouchard, Florent; Afsari, Bijan; Malick, Jérôme; Congedo, Marco: Approximate joint diagonalization with Riemannian optimization on the general linear group (2020)
  12. Chen, Shixiang; Ma, Shiqian; Man-Cho So, Anthony; Zhang, Tong: Proximal gradient method for nonsmooth optimization over the Stiefel manifold (2020)
  13. Eliasof, Moshe; Sharf, Andrei; Treister, Eran: Multimodal 3D shape reconstruction under calibration uncertainty using parametric level set methods (2020)
  14. Hong, Xia; Gao, Junbin; Chen, Sheng: Semi-blind joint channel estimation and data detection on sphere manifold for MIMO with high-order QAM signaling (2020)
  15. Hosseini, Reshad; Sra, Suvrit: An alternative to EM for Gaussian mixture models: batch and stochastic Riemannian optimization (2020)
  16. Hosseini, Reshad; Sra, Suvrit: Recent advances in stochastic Riemannian optimization (2020)
  17. Lieder, Felix: Solving large-scale cubic regularization by a generalized eigenvalue problem (2020)
  18. Li, Jiao-fen; Wen, Ya-qiong; Zhou, Xue-lin; Wang, Kai: Effective algorithms for solving trace minimization problem in multivariate statistics (2020)
  19. Liu, Changshuo; Boumal, Nicolas: Simple algorithms for optimization on Riemannian manifolds with constraints (2020)
  20. Lombard, John: Honey from the hives: a theoretical and computational exploration of combinatorial hives (2020)

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