Manopt, a Matlab toolbox for optimization on manifolds

TL;DR

Manopt is a user-friendly Matlab toolbox designed to facilitate the implementation and experimentation of Riemannian optimization algorithms for problems with structured constraints common in machine learning.

Contribution

The paper introduces Manopt, a Matlab toolbox that simplifies the application of optimization on manifolds, making advanced algorithms accessible to practitioners outside the research community.

Findings

Supports optimization problems with rank and orthogonality constraints

Enables efficient experimentation with state-of-the-art algorithms

Aims to broaden adoption of Riemannian optimization techniques

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 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.