Optimal control of partial differential equations

Summary

Optimal control of partial differential equations studies how to choose a control, such as a heat source or a boundary temperature. The aim is that the solution of a partial differential equation is as good as possible for a given cost. The state lives in an infinite-dimensional function space, such as a Sobolev space. It is the infinite-dimensional branch of optimal control and is also called PDE-constrained optimization. Its main tools are existence theory in function spaces, optimality systems with adjoint equations, and numerical methods such as the adjoint state method.