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 117 articles , 1 standard article )

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  1. Ronny Bergmann: Manopt.jl: Optimization on Manifolds in Julia (2022) not zbMATH
  2. Yamakawa, Yuya; Sato, Hiroyuki: Sequential optimality conditions for nonlinear optimization on Riemannian manifolds and a globally convergent augmented Lagrangian method (2022)
  3. Agarwal, Naman; Boumal, Nicolas; Bullins, Brian; Cartis, Coralia: Adaptive regularization with cubics on manifolds (2021)
  4. Bergmann, Ronny; Herzog, Roland; Silva Louzeiro, Maurício; Tenbrinck, Daniel; Vidal-Núñez, José: Fenchel duality theory and a primal-dual algorithm on Riemannian manifolds (2021)
  5. Breiding, Paul; Vannieuwenhoven, Nick: The condition number of Riemannian approximation problems (2021)
  6. Dong, Shuyu; Absil, P.-A.; Gallivan, K. A.: Riemannian gradient descent methods for graph-regularized matrix completion (2021)
  7. Dong, Yuexiao: A brief review of linear sufficient dimension reduction through optimization (2021)
  8. Fox, Jamie; Ökten, Giray: Brownian path generation and polynomial chaos (2021)
  9. Francisco, Juliano B.; Gonçalves, Douglas Soares; Viloche Bazán, Fermín S.; Paredes, Lila L. T.: Nonmonotone inexact restoration approach for minimization with orthogonality constraints (2021)
  10. Gao, Bin; Son, Nguyen Thanh; Absil, P.-A.; Stykel, Tatjana: Riemannian optimization on the symplectic Stiefel manifold (2021)
  11. Garcia-Salguero, Mercedes; Gonzalez-Jimenez, Javier: Fast and robust certifiable estimation of the relative pose between two calibrated cameras (2021)
  12. Heidarifar, Majid; Andrianesis, Panagiotis; Caramanis, Michael: A Riemannian optimization approach to the radial distribution network load flow problem (2021)
  13. Krumnow, Christian; Pfeffer, Max; Uschmajew, André: Computing eigenspaces with low rank constraints (2021)
  14. Li, Jiao-fen; Li, Wen; Duan, Xue-feng; Xiao, Mingqing: Newton’s method for the parameterized generalized eigenvalue problem with nonsquare matrix pencils (2021)
  15. Li, Ji; Cai, Jian-Feng; Zhao, Hongkai: Scalable incremental nonconvex optimization approach for phase retrieval (2021)
  16. Li, Xiaobo; Wang, Xianfu; Krishan Lal, Manish: A nonmonotone trust region method for unconstrained optimization problems on Riemannian manifolds (2021)
  17. Noferini, Vanni; Poloni, Federico: Nearest (\Omega)-stable matrix via Riemannian optimization (2021)
  18. Oviedo, Harry; Lara, Hugo: Spectral residual method for nonlinear equations on Riemannian manifolds (2021)
  19. Seth D. Axen, Mateusz Baran, Ronny Bergmann, Krzysztof Rzecki: Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds (2021) arXiv
  20. Sutti, Marco; Vandereycken, Bart: Riemannian multigrid line search for low-rank problems (2021)

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