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

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 GitHub repository
ManifoldsDiff.jl – a package to use (Euclidean) AD tools on manifolds, that also provides several differentials and gradients. GitHub repository
JuMP.jl can be used as interface to solve an optimization problem with Manopt. See usage examples. GitHub repository

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.

If you are also using Manifolds.jl please consider to cite

@article{AxenBaranBergmannRzecki:2023,
    AUTHOR     = {Seth D. Axen and Mateusz Baran and Ronny Bergmann and Krzysztof Rzecki},
    DOI        = {10.1145/3618296},
    EPRINT     = {2021.08777},
    EPRINTTYPE = {arXiv},
    JOURNAL    = {AMS Transactions on Mathematical Software},
    NOTE       = {accepted for publication},
    TITLE      = {Manifolds.jl: An Extensible {J}ulia Framework for Data Analysis on Manifolds},
    YEAR       = {2023}
}

as well. Note that all 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 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

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

odow/Manopt.jl

Manopt.jl

Getting started

Related packages

Citation

Further and Similar Packages & Links