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 33 articles , 1 standard article )

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  1. Paine, P. J.; Preston, Simon P.; Tsagris, M.; Wood, Andrew T. A.: An elliptically symmetric angular Gaussian distribution (2018)
  2. Bauer, Martin; Bruveris, Martins; Harms, Philipp; Møller-Andersen, Jakob: A numerical framework for Sobolev metrics on the space of curves (2017)
  3. Danaila, Ionut; Protas, Bartosz: Computation of ground states of the Gross-Pitaevskii functional via Riemannian optimization (2017)
  4. Horev, Inbal; Yger, Florian; Sugiyama, Masashi: Geometry-aware principal component analysis for symmetric positive definite matrices (2017)
  5. Hosseini, Seyedehsomayeh; Uschmajew, André: A Riemannian gradient sampling algorithm for nonsmooth optimization on manifolds (2017)
  6. Trendafilov, Nickolay T.; Fontanella, Sara; Adachi, Kohei: Sparse exploratory factor analysis (2017)
  7. Tron, Roberto; Daniilidis, Kostas: The space of essential matrices as a Riemannian quotient manifold (2017)
  8. Absil, P.-A.; Gousenbourger, Pierre-Yves; Striewski, Paul; Wirth, Benedikt: Differentiable piecewise-Bézier surfaces on Riemannian manifolds (2016)
  9. Balajewicz, Maciej; Tezaur, Irina; Dowell, Earl: Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier-Stokes equations (2016)
  10. Boumal, Nicolas: Nonconvex phase synchronization (2016)
  11. Cambier, Léopold; Absil, P.-A.: Robust low-rank matrix completion by Riemannian optimization (2016)
  12. Cherian, Anoop; Sra, Suvrit: Positive definite matrices: data representation and applications to computer vision (2016)
  13. De Sterck, Hans; Howse, Alexander: Nonlinearly preconditioned optimization on Grassmann manifolds for computing approximate Tucker tensor decompositions (2016)
  14. Mishra, Bamdev; Sepulchre, Rodolphe: Riemannian preconditioning (2016)
  15. Pölitz, Christian; Duivesteijn, Wouter; Morik, Katharina: Interpretable domain adaptation via optimization over the Stiefel manifold (2016)
  16. Sra, Suvrit; Hosseini, Reshad: Geometric optimization in machine learning (2016)
  17. Townsend, James; Koep, Niklas; Weichwald, Sebastian: Pymanopt: a python toolbox for optimization on manifolds using automatic differentiation (2016)
  18. Trendafilov, Nickolay T.; Gebru, Tsegay Gebrehiwot: Recipes for sparse LDA of horizontal data (2016)
  19. Wei, Hejie; Yang, Wei Hong: A Riemannian subspace limited-memory SR1 trust region method (2016)
  20. Absil, P.-A.; Oseledets, I.V.: Low-rank retractions: a survey and new results (2015)

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