PETSc TAO support for optimisation problems with FEniCSx

Variational formulations offer a robust foundation for solving partial differential equations. However, in practice, often additional requirements need to be imposed, such as bounds on material usage, stress constraints, geometric limitations, or manufacturing considerations, that cannot be addressed directly in an unconstrained setting. Constrained optimisation extends the variational approach by enabling the systematic inclusion of such real-world constraints. A collection of scalable and performant constrained optimization algorithms is available in the PETSc Toolkit for Advanced Optimization (TAO). FEniCSx provides a user-friendly environment for variational problems; however, it does currently not offer the same level of support for optimisation-specific routines. We demonstrate easy-to-use interoperability between FEniCSx and PETSc TAO within the convenience wrapper framework dolfiny, together with examples including (blocked) variational- and/or integral-, equality or inequality constraints.