Manopt, a matlab toolbox for optimization on manifolds

Nicolas Boumal, Bamdev Mishra, P. A. Absil, Rodolphe Sepulchre

Research output: Contribution to journalArticlepeer-review

671 Scopus citations


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 effcient 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. By dealing internally with most of the differential geometry, the package aims particularly at lowering the entrance barrier.

Original languageEnglish (US)
Pages (from-to)1455-1459
Number of pages5
JournalJournal of Machine Learning Research
StatePublished - Apr 2014

All Science Journal Classification (ASJC) codes

  • Software
  • Artificial Intelligence
  • Control and Systems Engineering
  • Statistics and Probability


  • Non convex
  • Nonlinear programming
  • Optimization with symmetries
  • Orthogonality constraints
  • Rank constraints
  • Riemannian optimization
  • Rotation matrices


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