Ronny Bergmann 

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141 Posts
Writes about research in optimisation & variational methods on manifolds, and numerics in Julia, where I develop Manifolds.jl and Manopt.jl.
Associate Professor at NTNU, Trondheim, Norway. Pixelfeed: @Kellertuer
🌐https://ronnybergmann.net
Languagesger/eng/nor
:orcid:https://orcid.org/0000-0001-8342-7218
GitHubhttps://github.com/kellertuer

Over the next few months I'll be applying for industry positions for data science and ML software engineering. Know of any great positions or interested in working with me? Let me know! https://sethaxen.com

My background is in bioinformatics. I've worked on many FOSS projects in Python, Julia, and C++, in particular for Bayesian inference and automatic differentiation. In my current role I help scientists use ML in their research through workshops, consultations, and software.

Seth Axen

🔈 Manopt.jl v0.4.54 🏔️

We introduce two new solvers:

• The Convex Bundle Method https://manoptjl.org/stable/solvers/convex_bundle_method/

• The Proximal Bundle Method https://manoptjl.org/stable/solvers/proximal_bundle_method/

to solve, (convex) nonsmooth optimization problems on Riemannian manifolds. The first one is also discussed in the paper “The Riemannian Convex Bundle Method” https://arxiv.org/abs/2402.13670.

Convex bundle method · Manopt.jl

Documentation for Manopt.jl.

Together with Roland Herzog and Hajg Jasa, we published a new algorithm to solve convex, non-smooth optimization problems on Riemannian manifolds:
The Riemannian Convex Bundle Method
Https://arxiv.org/abs/2402.13670

#Manopt #Julia #Optimization

The Riemannian Convex Bundle Method

We introduce the convex bundle method to solve convex, non-smooth optimization problems on Riemannian manifolds of bounded sectional curvature. Each step of our method is based on a model that involves the convex hull of previously collected subgradients, parallelly transported into the current serious iterate. This approach generalizes the dual form of classical bundle subproblems in Euclidean space. We prove that, under mild conditions, the convex bundle method converges to a minimizer. Several numerical examples implemented using Manopt.jl illustrate the performance of the proposed method and compare it to the subgradient method, the cyclic proximal point algorithm, as well as the proximal bundle method.

arXiv.org
Die Maus ist raus.
This week I was in the beautiful Schloss Hasenwinkel and have a talk about „Nonsmooth, nonconvex Optimization on Riemannian Manifolds“, covering some motivation and introduction as well. The slides are online at https://ronnybergmann.net/talks/2023-Hasenwinkel-Manopt.pdf

🔈 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 https://manoptjl.org/stable/tutorials/EmbeddingObjectives/

Define Objectives in the Embedding · Manopt.jl

Are you using Manifolds.jl or would like to learn how to use this package?
We now have a paper giving an introduction on Manifolds.jl – and comparing its efficientcy to other packages implementing Riemannian manifolds

S. D. Axen, M. Baran, R. Bergmann, K. Rzecki
“Manifolds.jl: An Extensible Julia Framework for Data Analysis on Manifolds”, ACM TOMS, http://dx.doi.org/10.1145/3618296

Since Manopt 0.4.32 we have a new solver: During his master thesis Mathias investigated the ARC (adaptive regularization with cubics) solver and brought it to Julia! See https://manoptjl.org/stable/solvers/adaptive-regularization-with-cubics/ for details. Thanks Mathias!
Adaptive Regularization with Cubics · Manopt.jl

Tomorrow I will give a(n online) talk at the ICIAM within the minisymposium “Approximation and modeling with manifold-valued data” about the Riemannian DC algorithm
at 18:05 JST (11:05 CEST). The slides are already online at https://ronnybergmann.net/talks/2023-ICIAM-Difference-of-Convex.pdf #Manifolds #ICIAM #Optimization
ManifoldsBase.jl 0.14.10 introduces an interface to implement `Weigarten(M, p, X, V)` maps (https://juliamanifolds.github.io/ManifoldsBase.jl/dev/functions/#ManifoldsBase.Weingarten-Tuple{AbstractManifold,%20Any,%20Any,%20Any}).
Together with the new ManifoldDiff.jl 0.3.6 this allows for a generic implementation of a conversion from Euclidean to Riemannian Hessians for embedded submanifolds, see https://juliamanifolds.github.io/ManifoldDiff.jl/dev/library/#ManifoldDiff.riemannian_Hessian-Tuple{AbstractManifold,%20Any,%20Any,%20Any,%20Any}. #Manifolds #Julia
Basic functions · ManifoldsBase.jl