PDE-constrained optimization using JuliaSmoothOptimizers

In this presentation, we showcase a new optimization infrastructure within JuliaSmoothOptimizers for PDE-constrained optimization problems in Julia. We introduce PDENLPModels.jl a package that discretizes PDE-constrained optimization problems using finite elements methods via Gridap.jl. The resulting problem can then be solved by solvers tailored for large-scale optimization implemented in pure Julia such as DCISolver.jl and FletcherPenaltyNLPSolver.jl.

The study of algorithms for optimization problems has become the backbone of data science and its multiple applications. Nowadays, new challenges involve ever-increasing amounts of data and model complexity. Examples include optimization problems constrained by partial differential equations (PDE) that are frequent in imaging, signal processing, shape optimization, and seismic inversion. In this presentation, we showcase a new optimization infrastructure to model and solve PDE-constrained problems in the Julia programming language. We build upon the JuliaSmoothOptimizers infrastructure for modeling and solving continuous optimization problems. We introduce PDENLPModels.jl a package that discretizes PDE-constrained optimization problems using finite elements methods via Gridap.jl. The resulting problem can then be solved by solvers tailored for large-scale optimization implemented in pure Julia such as DCISolver.jl and FletcherPenaltyNLPSolver.jl.