02/10/2025 –, Amphithéâtre Robert Faure
Langue: English
Optimal control problems of ordinary differential equations are challenging numerical problems to solve with applications in many fields, including a current strong trend in quantum control. The aim of this talk is to present the ongoing effort made in the framework of control-toolbox.org with the Julia package OptimalControl.jl, within a collaboration involving Inria, CNRS and Argonne. The focus will be on so-called direct methods that discretise the control problem into a large sparse nonlinear mathematical program. The numerical solution then heavily relies on sparse automatic differentiation (AD) and sparse numerical linear algebra for optimisation solvers. This includes remarkable progress in Julia with such packages as Enzyme.jl, ADNLPModels.jl, ExaModels.jl or MadNLP.jl. The last two packages, in particular, allow to take advantage of the natural massive SIMD parallelism of the discretised problem to provide efficient solving on GPU's.
The specific structure of the discretised math program problem raises challenging issues in terms of sparsity detection for AD, numerical linear algebra and optimisation. Going to GPU also implies strong modelling and discretisation choices to achieve efficient solving for a large number of variables and constraints. These topics are at the heart of a beginning collaboration involving people from Inria (McTAO team) and Argonne (notably A. Montoison), and also benefits from an existing JLESC project between the two institutions ("Shared Infrastructure for Source Transformation Automatic Differentiation").
Professor of applied math at Université Côte d’Azur, CNRS, Inria, LJAD
Scientific interests - Optimisation and control: geometry, algorithms, applications