mlsanityData to 14 Oct 2026

Manopt, a Matlab toolbox for optimization on manifolds

arXiv 1308.5200 ↗First posted 23 Aug 2013cs.MS cs.LG math.OCcited by 113

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Abstract (arXiv)

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 www.manopt.org, 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.

Key facts. Cited by 113 papers in the map (data through 14 Oct 2026). First posted on arXiv 23 Aug 2013.

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Citing papers per year: 2021: 30; 2022: 21; 2023: 17; 2024: 12; 2025: 22; 2026: 11.

113 papers.

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  1. 2021Edge Artificial Intelligence for 6G: Vision, Enabling Technologies, and Applicationscited by 97
  2. 2021Universal Approximation Theorems for Differentiable Geometric Deep Learningcited by 41
  3. 2021Tangent Space Backpropagation for 3D Transformation Groupscited by 40
  4. 2021On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometrycited by 32
  5. 2022Bayesian Learning for Neural Networks: an algorithmic surveycited by 23
  6. 2021Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matricescited by 22
  7. 2021Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimizationcited by 21
  8. 2023A Survey of Geometric Optimization for Deep Learning: From Euclidean Space to Riemannian Manifoldcited by 21
  9. 2025PoLAR: Polar-Decomposed Low-Rank Adapter Representationcited by 20
  10. 2024Synchronization on circles and spheres with nonlinear interactionscited by 17
  11. 2025Understanding and Improving Shampoo and SOAP via Kullback-Leibler Minimizationcited by 16
  12. 2021A Scalable Second Order Method for Ill-Conditioned Matrix Completion from Few Samplescited by 13
38 more
  1. 2022Federated Learning on Riemannian Manifoldscited by 13
  2. 2021Interactive Dimensionality Reduction for Comparative Analysiscited by 12
  3. 2022Riemannian Hamiltonian methods for min-max optimization on manifoldscited by 12
  4. 2022Differentially private Riemannian optimizationcited by 12
  5. 2021An Inexact Projected Gradient Method with Rounding and Lifting by Nonlinear Programming for Solving Rank-One Semidefinite Relaxation of Polynomial Optimizationcited by 10
  6. 2021Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometrycited by 10
  7. 2022First-Order Algorithms for Min-Max Optimization in Geodesic Metric Spacescited by 10
  8. 2022MMES: Mixture Model based Evolution Strategy for Large-Scale Optimizationcited by 9
  9. 2023Chordal Averaging on Flag Manifolds and Its Applicationscited by 9
  10. 2025Causal Abstraction Learning based on the Semantic Embedding Principlecited by 9
  11. 2025SECA: Semantically Equivalent and Coherent Attacks for Eliciting LLM Hallucinationscited by 9
  12. 2021Manifold optimization for non-linear optimal transport problemscited by 8
  13. 2023Alignment of Density Maps in Wasserstein Distancecited by 8
  14. 2025Building Rome with Convex Optimizationcited by 8
  15. 2021An Online Riemannian PCA for Stochastic Canonical Correlation Analysiscited by 7
  16. 2022Riemannian block SPD coupling manifold and its application to optimal transportcited by 7
  17. 2022Semantic keypoint-based pose estimation from single RGB framescited by 7
  18. 2022NCVX: A General-Purpose Optimization Solver for Constrained Machine and Deep Learningcited by 7
  19. 2022Multi-View Independent Component Analysis with Shared and Individual Sourcescited by 7
  20. 2023Zeroth-order Riemannian Averaging Stochastic Approximation Algorithmscited by 7
  21. 2021Sparse Quadratic Optimisation over the Stiefel Manifold with Application to Permutation Synchronisationcited by 6
  22. 2025SPD Matrix Learning for Neuroimaging Analysis: Perspectives, Methods, and Challengescited by 6
  23. 2021Fast and Robust Certifiable Estimation of the Relative Pose Between Two Calibrated Camerascited by 5
  24. 2021Terahertz-Band Joint Ultra-Massive MIMO Radar-Communications: Model-Based and Model-Free Hybrid Beamformingcited by 5
  25. 2021tensorflow-riemopt: A Library for Optimization on Riemannian Manifoldscited by 5
  26. 2021NCVX: A User-Friendly and Scalable Package for Nonconvex Optimization in Machine Learningcited by 5
  27. 2022Accelerating nuclear-norm regularized low-rank matrix optimization through Burer-Monteiro decompositioncited by 5
  28. 2022Riemannian accelerated gradient methods via extrapolationcited by 5
  29. 2023Differential geometry with extreme eigenvalues in the positive semidefinite conecited by 5
  30. 2024Federated Learning on Riemannian Manifolds with Differential Privacycited by 5
  31. 2024Nonconvex Federated Learning on Compact Smooth Submanifolds With Heterogeneous Datacited by 5
  32. 2024An Overview of the Burer-Monteiro Method for Certifiable Robot Perceptioncited by 5
  33. 2025Riemannian Optimization on Relaxed Indicator Matrix Manifoldcited by 5
  34. 2021New Riemannian preconditioned algorithms for tensor completion via polyadic decompositioncited by 4
  35. 2023Capacity Bounds for Hyperbolic Neural Network Representations of Latent Tree Structurescited by 4
  36. 2023Fast, Scalable, Warm-Start Semidefinite Programming with Spectral Bundling and Sketchingcited by 4
  37. 2024Riemannian coordinate descent algorithms on matrix manifoldscited by 4
  38. 2024Riemannian Federated Learning via Averaging Gradient Streamscited by 4

50 most cited of 113 All 113 (JSON)