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 22 articles , 1 standard article )

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  1. Absil, P.-A.; Gousenbourger, Pierre-Yves; Striewski, Paul; Wirth, Benedikt: Differentiable piecewise-Bézier surfaces on Riemannian manifolds (2016)
  2. Boumal, Nicolas: Nonconvex phase synchronization (2016)
  3. Cambier, Léopold; Absil, P.-A.: Robust low-rank matrix completion by Riemannian optimization (2016)
  4. Cherian, Anoop; Sra, Suvrit: Positive definite matrices: data representation and applications to computer vision (2016)
  5. De Sterck, Hans; Howse, Alexander: Nonlinearly preconditioned optimization on Grassmann manifolds for computing approximate Tucker tensor decompositions (2016)
  6. Mishra, Bamdev; Sepulchre, Rodolphe: Riemannian preconditioning (2016)
  7. Pölitz, Christian; Duivesteijn, Wouter; Morik, Katharina: Interpretable domain adaptation via optimization over the Stiefel manifold (2016)
  8. Sra, Suvrit; Hosseini, Reshad: Geometric optimization in machine learning (2016)
  9. Townsend, James; Koep, Niklas; Weichwald, Sebastian: Pymanopt: a python toolbox for optimization on manifolds using automatic differentiation (2016)
  10. Trendafilov, Nickolay T.; Gebru, Tsegay Gebrehiwot: Recipes for sparse LDA of horizontal data (2016)
  11. Absil, P.-A.; Oseledets, I.V.: Low-rank retractions: a survey and new results (2015)
  12. Boumal, Nicolas; Absil, P.-A.: Low-rank matrix completion via preconditioned optimization on the Grassmann manifold (2015)
  13. Chaudhury, K.N.; Khoo, Y.; Singer, A.: Global registration of multiple point clouds using semidefinite programming (2015)
  14. Cunningham, John P.; Ghahramani, Zoubin: Linear dimensionality reduction: survey, insights, and generalizations (2015)
  15. Hintermüller, Michael; Wu, Tao: Robust principal component pursuit via inexact alternating minimization on matrix manifolds (2015)
  16. Huang, Wen; Absil, P.-A.; Gallivan, K.A.: A Riemannian symmetric rank-one trust-region method (2015)
  17. Liu, Xin-Guo; Wang, Xue-Feng; Wang, Wei-Guo: Maximization of matrix trace function of product Stiefel manifolds (2015)
  18. Sra, Suvrit; Hosseini, Reshad: Conic geometric optimization on the manifold of positive definite matrices (2015)
  19. Absil, P.-A.; Amodei, Luca; Meyer, Gilles: Two Newton methods on the manifold of fixed-rank matrices endowed with Riemannian quotient geometries (2014)
  20. Boumal, Nicolas; Mishra, Bamdev; Absil, P.-A.; Sepulchre, Rodolphe: Manopt, a Matlab toolbox for optimization on manifolds (2014)

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