Manopt.jl

Optimization Algorithm on Riemannian Manifolds.

For a function $f: ℳ → ℝ$ that maps from a Riemannian manifold ℳ to the real line, we aim to solve

Find the minimizer p on ℳ, i.e. the (or a) point where f attains its minimum.

Manopt.jl provides

• A framework to implement arbitrary optimization algorithms on Riemannian Manifolds
• A library of optimization algorithms on Riemannian manifolds
• an easy-to-use interface for (debug) output and recording values during an algorithm run.
• several tools to investigate the algorithms, gradients, and optimality criteria

Getting started

In Julia you can get started by just typing

julia using Pkg; Pkg.add("Manopt");

and then checkout the Get Started: Optimize! tutorial.

Related packages

Manopt.jl is based on ManifoldsBase.jl, hence the algorithms can be used with any manifold following this interface for defining a Riemannian manifold.

The following packages are related to Manopt.jl

• Manifolds.jl – a library of manifolds implemented using ManifoldsBase.jl :octocat: GitHub repository
• ManifoldsDiff.jl – a package to use (Euclidean) AD tools on manifolds, that also provides several differentials and gradients. :octocat: GitHub repository

Citation

If you use Manopt.jl in your work, please cite the following

biblatex @article{Bergmann2022, Author = {Ronny Bergmann}, Doi = {10.21105/joss.03866}, Journal = {Journal of Open Source Software}, Number = {70}, Pages = {3866}, Publisher = {The Open Journal}, Title = {Manopt.jl: Optimization on Manifolds in {J}ulia}, Volume = {7}, Year = {2022}, }

To refer to a certain version or the source code in general we recommend to cite for example

biblatex @software{manoptjl-zenodo-mostrecent, Author = {Ronny Bergmann}, Copyright = {MIT License}, Doi = {10.5281/zenodo.4290905}, Publisher = {Zenodo}, Title = {Manopt.jl}, Year = {2022}, }

for the most recent version or a corresponding version specific DOI, see the list of all versions. Note that both citations are in BibLaTeX format.

Further and Similar Packages & Links

Manopt.jl belongs to the Manopt family:

• manopt.org – The Matlab version of Manopt, see also their :octocat: GitHub repository
• pymanopt.org – The Python version of Manopt – providing also several AD backends, see also their :octocat: GitHub repository

but there are also more packages providing tools on manifolds:

• Jax Geometry (Python/Jax) for differential geometry and stochastic dynamics with deep learning
• Geomstats (Python with several backends) focusing on statistics and machine learning :octocat: GitHub repository
• Geoopt (Python & PyTorch) – Riemannian ADAM & SGD. :octocat: GitHub repository
• McTorch (Python & PyToch) – Riemannian SGD, Adagrad, ASA & CG.
• ROPTLIB (C++) a Riemannian OPTimization LIBrary :octocat: GitHub repository
• TF Riemopt (Python & TensorFlow) Riemannian optimization using TensorFlow

Did you use Manopt.jl somewhere? Let us know! We'd love to collect those here as well.