A Brief Introduction to PDE-Constrained Optimization

Abstract

In this chapter we give a brief overview of optimization problems with partial differential equation (PDE) constraints, i.e., PDE constrained optimiza- tion (PDECO). We start with three potentially different formulations of a general PDECO problem and focus on the so called reduced form. We present a derivation of the optimality conditions. Later we discuss the linear and the semilinear quadratic PDECO problems. We conclude with the discretization and the convergence rates for these problems. For illustration, we make a Matlab code available at https://bitbucket.org/harbirantil/pde constrained opt that solves the semilinear PDEO problem with control constraints.