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 28 articles , 1 standard article )

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  1. Bauer, Martin; Bruveris, Martins; Harms, Philipp; Møller-Andersen, Jakob: A numerical framework for Sobolev metrics on the space of curves (2017)
  2. Hosseini, Seyedehsomayeh; Uschmajew, André: A Riemannian gradient sampling algorithm for nonsmooth optimization on manifolds (2017)
  3. Absil, P.-A.; Gousenbourger, Pierre-Yves; Striewski, Paul; Wirth, Benedikt: Differentiable piecewise-Bézier surfaces on Riemannian manifolds (2016)
  4. 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)
  5. Boumal, Nicolas: Nonconvex phase synchronization (2016)
  6. Cambier, Léopold; Absil, P.-A.: Robust low-rank matrix completion by Riemannian optimization (2016)
  7. Cherian, Anoop; Sra, Suvrit: Positive definite matrices: data representation and applications to computer vision (2016)
  8. De Sterck, Hans; Howse, Alexander: Nonlinearly preconditioned optimization on Grassmann manifolds for computing approximate Tucker tensor decompositions (2016)
  9. Mishra, Bamdev; Sepulchre, Rodolphe: Riemannian preconditioning (2016)
  10. Pölitz, Christian; Duivesteijn, Wouter; Morik, Katharina: Interpretable domain adaptation via optimization over the Stiefel manifold (2016)
  11. Sra, Suvrit; Hosseini, Reshad: Geometric optimization in machine learning (2016)
  12. Townsend, James; Koep, Niklas; Weichwald, Sebastian: Pymanopt: a python toolbox for optimization on manifolds using automatic differentiation (2016)
  13. Trendafilov, Nickolay T.; Gebru, Tsegay Gebrehiwot: Recipes for sparse LDA of horizontal data (2016)
  14. Wei, Hejie; Yang, Wei Hong: A Riemannian subspace limited-memory SR1 trust region method (2016)
  15. Absil, P.-A.; Oseledets, I.V.: Low-rank retractions: a survey and new results (2015)
  16. Boumal, Nicolas: Riemannian trust regions with finite-difference Hessian approximations are globally convergent (2015)
  17. Boumal, Nicolas; Absil, P.-A.: Low-rank matrix completion via preconditioned optimization on the Grassmann manifold (2015)
  18. Chaudhury, K.N.; Khoo, Y.; Singer, A.: Global registration of multiple point clouds using semidefinite programming (2015)
  19. Cunningham, John P.; Ghahramani, Zoubin: Linear dimensionality reduction: survey, insights, and generalizations (2015)
  20. Hintermüller, Michael; Wu, Tao: Robust principal component pursuit via inexact alternating minimization on matrix manifolds (2015)

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