  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.
