Manopt, a Matlab toolbox for optimization on manifolds
This provides a user-friendly tool for researchers and practitioners in machine learning to handle optimization problems with rank and orthogonality constraints, though it is incremental as it packages existing algorithms into a toolbox.
The authors tackled the challenge of applying optimization on manifolds to machine learning problems with structured constraints by developing Manopt, a Matlab toolbox that simplifies experimenting with state-of-the-art Riemannian optimization algorithms, making it accessible to practitioners outside the field.
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.