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https://github.com/JuliaManifolds/Manopt.jl

🏔️Manopt. jl – Optimization on Manifolds in Julia
https://github.com/JuliaManifolds/Manopt.jl

julia manifolds manopt optimization

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🏔️Manopt. jl – Optimization on Manifolds in Julia

Host: GitHub
URL: https://github.com/JuliaManifolds/Manopt.jl
Owner: JuliaManifolds
License: other
Created: 2016-11-25T10:00:20.000Z (almost 8 years ago)
Default Branch: master
Last Pushed: 2024-04-13T15:37:58.000Z (7 months ago)
Last Synced: 2024-04-14T08:50:29.101Z (7 months ago)
Topics: julia, manifolds, manopt, optimization
Language: Julia
Homepage: http://manoptjl.org
Size: 48.5 MB
Stars: 287
Watchers: 13
Forks: 39
Open Issues: 13
Metadata Files:
- Readme: Readme.md
- Changelog: Changelog.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
- Citation: CITATION.bib

Awesome Lists containing this project

awesome-sciml - JuliaManifolds/Manopt.jl: Optimization on Manifolds in Julia

README

        


    

        

      

    



## Optimization Algorithm on Riemannian Manifolds.

[![](https://img.shields.io/badge/docs-stable-blue?logo=Julia&logoColor=white)](https://manoptjl.org/stable)

[![Code Style: Blue](https://img.shields.io/badge/code%20style-blue-4495d1.svg)](https://github.com/invenia/BlueStyle)

[![CI](https://github.com/JuliaManifolds/Manopt.jl/workflows/CI/badge.svg)](https://github.com/JuliaManifolds/Manopt.jl/actions?query=workflow%3ACI+branch%3Amaster)

[![codecov](https://codecov.io/gh/JuliaManifolds/Manopt.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaManifolds/Manopt.jl)

[![Aqua QA](https://raw.githubusercontent.com/JuliaTesting/Aqua.jl/master/badge.svg)](https://github.com/JuliaTesting/Aqua.jl)

[![DOI](https://zenodo.org/badge/74746729.svg)](https://zenodo.org/badge/latestdoi/74746729)

[![DOI](https://joss.theoj.org/papers/10.21105/joss.03866/status.svg)](https://doi.org/10.21105/joss.03866)

For a function $f: ℳ → ℝ$  that maps from a [Riemannian manifold](https://en.wikipedia.org/wiki/Riemannian_manifold)

ℳ to the real line, this package aims to solve

> Find the minimizer p on ℳ, that is, 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!](https://manoptjl.org/stable/tutorials/Optimize/) tutorial.

## Related packages

Manopt.jl is based on [`ManifoldsBase.jl`](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/),

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`](https://juliamanifolds.github.io/Manifolds.jl/stable/): a library of manifolds implemented using [`ManifoldsBase.jl`](https://juliamanifolds.github.io/ManifoldsBase.jl/stable/) :octocat: [GitHub repository](https://github.com/JuliaManifolds/Manifolds.jl)

* [`ManifoldsDiff.jl`](https://juliamanifolds.github.io/ManifoldDiff.jl/stable/): a package to use (Euclidean) AD tools on manifolds, that also provides several differentials and gradients. :octocat: [GitHub repository](https://github.com/JuliaManifolds/ManifoldDiff.jl)

* [`JuMP.jl`](https://jump.dev/): can be used as interface to solve an optimization problem with Manopt. See [usage examples](https://manoptjl.org/stable/extensions/). :octocat: [GitHub repository](https://github.com/jump-dev/JuMP.jl)

## 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 please 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      = {2024},

}

```

for the most recent version or a corresponding version specific DOI, see [the list of all versions](https://zenodo.org/search?page=1&size=20&q=conceptrecid:%224290905%22&sort=-version&all_versions=True).

If you are also using [`Manifolds.jl`](https://juliamanifolds.github.io/Manifolds.jl/stable/) please consider to cite

```biblatex

@article{AxenBaranBergmannRzecki:2023,

    AUTHOR    = {Axen, Seth D. and Baran, Mateusz and Bergmann, Ronny and Rzecki, Krzysztof},

    ARTICLENO = {33},

    DOI       = {10.1145/3618296},

    JOURNAL   = {ACM Transactions on Mathematical Software},

    MONTH     = {dec},

    NUMBER    = {4},

    TITLE     = {Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds},

    VOLUME    = {49},

    YEAR      = {2023}

}

```

as well.

Note that all citations are in [BibLaTeX](https://ctan.org/pkg/biblatex) format.

`Manopt.jl` belongs to the Manopt family:

* [www.manopt.org](https://www.manopt.org): the MATLAB version of Manopt, see also their :octocat: [GitHub repository](https://github.com/NicolasBoumal/manopt)

* [www.pymanopt.org](https://www.pymanopt.org): the Python version of Manopt—providing also several AD backends, see also their :octocat: [GitHub repository](https://github.com/pymanopt/pymanopt)

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