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 84 articles , 1 standard article )

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  1. 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)
  2. Bendory, Tamir; Edidin, Dan; Eldar, Yonina C.: On signal reconstruction from FROG measurements (2020)
  3. Bortoloti, Marcio Antônio de A.; Fernandes, Teles A.; Ferreira, Orizon P.; Yuan, Jinyun: Damped Newton’s method on Riemannian manifolds (2020)
  4. Bouchard, Florent; Afsari, Bijan; Malick, Jérôme; Congedo, Marco: Approximate joint diagonalization with Riemannian optimization on the general linear group (2020)
  5. Chen, Shixiang; Ma, Shiqian; Man-Cho So, Anthony; Zhang, Tong: Proximal gradient method for nonsmooth optimization over the Stiefel manifold (2020)
  6. Eliasof, Moshe; Sharf, Andrei; Treister, Eran: Multimodal 3D shape reconstruction under calibration uncertainty using parametric level set methods (2020)
  7. 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)
  8. Hosseini, Reshad; Sra, Suvrit: An alternative to EM for Gaussian mixture models: batch and stochastic Riemannian optimization (2020)
  9. Hosseini, Reshad; Sra, Suvrit: Recent advances in stochastic Riemannian optimization (2020)
  10. Massart, Estelle; Absil, P.-A.: Quotient geometry with simple geodesics for the manifold of fixed-rank positive-semidefinite matrices (2020)
  11. Nava-Yazdani, Esfandiar; Hege, Hans-Christian; Sullivan, T. J.; von Tycowicz, Christoph: Geodesic analysis in Kendall’s shape space with epidemiological applications (2020)
  12. Storath, Martin; Weinmann, Andreas: Wavelet sparse regularization for manifold-valued data (2020)
  13. Usevich, Konstantin; Li, Jianze; Comon, Pierre: Approximate matrix and tensor diagonalization by unitary transformations: convergence of Jacobi-type algorithms (2020)
  14. Bendory, Tamir; Boumal, Nicolas; Leeb, William; Levin, Eitan; Singer, Amit: Multi-target detection with application to cryo-electron microscopy (2019)
  15. Bergmann, R.; Laus, F.; Persch, J.; Steidl, G.: Recent advances in denoising of manifold-valued images (2019)
  16. Ehler, Martin; Gräf, Manuel: Reproducing kernels for the irreducible components of polynomial spaces on unions of Grassmannians (2019)
  17. Feng, Shoubo; Ren, Weijie; Han, Min; Chen, Yen Wei: Robust manifold broad learning system for large-scale noisy chaotic time series prediction: a perturbation perspective (2019)
  18. Gousenbourger, Pierre-Yves; Massart, Estelle; Absil, P.-A.: Data fitting on manifolds with composite Bézier-like curves and blended cubic splines (2019)
  19. Hofmeyr, David P.; Pavlidis, Nicos G.; Eckley, Idris A.: Minimum spectral connectivity projection pursuit. Divisive clustering using optimal projections for spectral clustering (2019)
  20. Hosseini, Seyedehsomayeh; Uschmajew, André: A gradient sampling method on algebraic varieties and application to nonsmooth low-rank optimization (2019)

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