Hajg Jasa, Ronny Bergmann, Christian K\"ummerle, Avanti Athreya, Zachary Lubberts: Procrustes Problems on Random Matrices https://arxiv.org/abs/2510.05182 https://arxiv.org/pdf/2510.05182 https://arxiv.org/html/2510.05182

On Manifolds, the gradient depends on the Riemannian metric, the differential does not. For a costly metric, using the gradient for the differential might be costly.

Manopt.jl 0.5.19 now offers first order objectives with dedicated implementations of differentials:

manoptjl.org/stable/plans...

We have a new package nearly ready to be registered. GeometricKalman.jl – state estimation on non-Euclidean spaces. You can already read the arXiv preprint:

We have a new package! LieGroups.jl juliamanifolds.github.io/LieGroups.jl... provides Lie groups based in Manifolds.jl. See the full announcement at discourse.julialang.org/t/ann-liegro...

The newest version of Manopt.jl – 0.5.12 introduces a new algorithm: The gradient projection method. See
manoptjl.org/stable/solve...
as well as the arXiv preprint
arxiv.org/abs/2504.11815

#Manifolds #julialang #Manopt

In the new version Manopt.jl v0.5.7 we introduce the

Mesh Adaptive Direct Reach (MADS) algorithm(s)
manoptjl.org/stable/solve...

mainly providing the LTMADS which @oddsen.bsky.social worked on in his masters thesis.

Thanks Sander!

#Manifolds #julialang #Manopt

We started a monthly community call recently!

The next one is coming Tuesday, 16.00 (4pm) CET. You can find the zoom link on discourse

discourse.julialang.org/t/juliamanif...

Short reintroduction for all my new followers:

Hi! 👋
I work on numerical methods and optimization involving Riemannian manifolds #mathsky. I am a fan of #julialang, so I also implement these methods in Julia.

Sometimes I take detours into documentation, e.g. with Quarto, for reproducible research.

🔈 Manopt.jl v0.4.54 🏔️

We introduce two new solvers:

• The Convex Bundle Method manoptjl.org/stable/solve...
• The Proximal Bundle Method manoptjl.org/stable/solve...

to solve, (convex) nonsmooth optimization problems on Riemannian manifolds. The first one is also discussed in the paper from

If you are working with Manifolds.jl or want to learn what it is and how to use it, our paper was published last week: dl.acm.org/doi/10.1145/...

We now have a new (aggregated) home!

juliamanifolds.github.io

is an aggregation of all manifold related packages. While each package still has their URL for an individual documentation, this common place especially features a global search over all these packages.

The new version of Manopt.jl – 0.4.42 – adds an extension that allows algorithms from Manopt.jl together with manifolds fron Manifolds.jl within jump.dev !

Check out manoptjl.org/stable/exten... for an example and the full documentation.

🔈Manifolds.jl 0.9

We now offer Manifolds with static or dynamic parameters! The first (classical) ones are super fast. The new ones might compile a bit faster and are more flexible while being not much slower.

See all changes and what might break your previous code at
github.com/JuliaManifol...

🔈 ManifoldsBase.jl v0.15
After quite a while – it was time for a major update

* TangentSpace and ProductManifold are now already available in ManifoldsBase
* several aspects were unified, e.g. allocation and error messages.

See all changes at github.com/JuliaManifol...

🔈 Manopt.jl v0.4.34 🏔️
introduces the keyword `objective_type=:Euclidean`,
which allows you to provide a Euclidean cost, gradient, Hessian in the embedding of a manifold,
we then perform the conversion to Riemannian gradient and Hessian automatically in Manopt.jl
See manoptjl.org/stable/tutor...

If you wuld like to learn how to use Manifolds.jl
we now have a paper giving an introduction and comparison to other packages.

S. D. Axen, M. Baran, R. Bergmann, K. Rzecki
“Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds”, ACM TOMS, dx.doi.org/10.1145/3618...