Abstract
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 www.manopt.org, 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 language | English (US) |
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Pages (from-to) | 1455-1459 |
Number of pages | 5 |
Journal | Journal of Machine Learning Research |
Volume | 15 |
State | Published - Apr 2014 |
All Science Journal Classification (ASJC) codes
- Software
- Artificial Intelligence
- Control and Systems Engineering
- Statistics and Probability
Keywords
- Non convex
- Nonlinear programming
- Optimization with symmetries
- Orthogonality constraints
- Rank constraints
- Riemannian optimization
- Rotation matrices