Automating convex optimization problems in FEniCSx

Convex optimization problems arise in many fields of physics, applied mathematics, fluid and solid mechanics or even mathematical finance. Interesting applications usually involve non-smooth terms which require well-designed optimization algorithms for their resolution. In this work, we consider PDE-based non-smooth convex optimization problems and present a Python package built on top of the FEniCSx finite element library. We leverage conic representation of convex functions to design a domain-specific language which enables to automate the formulation, discretization and resolution of non-smooth convex problems. The resulting conic problems are solved by the primal-dual interior-point solver Mosek. We finally present various applications regarding viscoplastic fluids, elastoplastic solids, topology optimization and form-finding of optimal shells.

• Github repository: https://github.com/bleyerj/dolfinx_optim
• Online documentation: https://bleyerj.github.io/dolfinx_optim/