Tangi Migot

Tangi Migot

Computational Mathematician

Partially differentiable projects

1 minute read

Published:

I am starting a new year in Montreal and one of the main projects for this year is to move forward in finalizing an ecosystem for optimization problems with partial differential equations in the constraints. The ecosystem is hosted under the JuliaSmoothOptimizers umbrella and contains:

As usual modeling packages are fun, but not more than new solvers! I am focusing on two packages:

  • Fletcher’s penalty method. This method is matrix-free, which would be just perfect for huge large-scale structured problems such as PDE-constrained problems. The cherry on top of the cake is that this package uses Stopping.
  • DCISolver. This package uses a matrix-free feasibility process, but the tangent step still relies on an SQD matrix factorization using HSL or LDLFactorizations. Still, it is showing great performance even on large problems. I wrote a tutorial on jso-docs.github.io showing a comparison with Ipopt on a distributed Poisson control problem with Dirichlet boundary conditions (Spoiler alert: DCI is doing great). You can also play with a similar example on mybinder.org via the package’s documentation.

You can check the talk I gave at IVADO last October, on youtube.

The whole ecosystem is already in advanced testing and being used in my teaching at Polytechnique Montreal.

Upcoming

  • Upgrade of PDENLPModels to Gridap 0.17 (which shows great performance improvements last JuliaCon New tools to solve PDEs in Julia with Gridap.jl).
  • As usual, more problems and applications for PDEOptimizationProblems :).
  • DCISolver is under review in the Journal of Open Source Software. The whole review process was pretty fun (for once) and helped improve the package’s documentation. Hoping for the good news soon.
  • Why does FPS use Stopping?

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ARCqK published in Mathematical Programming

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Published:

I am thrilled to share that the article Scalable adaptive cubic regularization methods has been published in the journal Mathematical Programming, Series A. This has been a really exciting journey with my co-authors Jean-Pierre Dussault and Dominique Orban on this really exciting work that I hope will help explore the numerical possibilities of ARC methods. The proposed implementation is a perfect fit for large-scale application as it solves the subproblem inexactly and only required Hessian-vector products, so no need to evaluate and store the Hessian matrix. As usual, the code has been done in Julia and is available in the folder paper in the Github repository AdaptiveRegularization.jl. Full text published version available from here, enjoy!

Looking Back at the Winter Session

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In the world of numerical optimization, the quest for efficiency, accuracy, and innovation never ceases. At Polytechnique Montréal, students embarking on their educational journey have a unique opportunity to explore this dynamic field through the course MTH8408 Méthodes d’optimisation et contrôle optimal. This course, which I had the privilege of teaching during the winter session of 2023, delves into the depths of numerical methods for optimization, variational calculus, and optimal control.

Unveiling JuliaSmoothOptimizers at JuMP-dev Workshop, JuliaCon 2023

2 minute read

Published:

I am thrilled to share my experiences from the recent JuMP-dev workshop that took place at the JuliaCon 2023, held at MIT in Boston, USA. As a passionate researcher in the field of numerical optimization, this year’s conference was particularly special for me, as it marked my first in-person attendance after the previous year’s online edition (read about it here). You can check the replay of my talk on youtube.

PDENLPModels.jl published in JOSS

4 minute read

Published:

I am very happy to announce the publication in the Journal of Open Source Software of the paper PDENLPModels.jl: A NLPModel API for optimization problems with PDE-constraints.