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 x 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

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

and then checkout the Get Started: Optimize! tutorial.

Manopt.jl is based on ManifoldsBase.jl, hence the algorithms can be used with any manifold defined e.g. within Manifolds.jl.

Further Packages & Links

Manopt.jl belongs to the Manopt family:

• manopt.org – The Matlab version of Manopt, see also their GitHub repository
• pymanopt.org – The Python version of Manopt – providing also several AD backends, see also their 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 GitHub repository
• Geoopt (Python & PyTorch) – Riemannian ADAM & SGD. GitHub repository
• McTorch (Python & PyToch) – Riemannian SGD, Adagrad, ASA & CG.
• ROPTLIB (C++) a Riemannian OPTimization LIBrary GitHub repository
• TF Riemopt (Python & TensorFlow) Riemannian optimization using TensorFlow

Citation

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

@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

@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.