Model Problems in PDE-Constrained Optimization

This work aims to aid in introducing, experimenting and benchmarking algorithms for PDE-constrained optimization problems by presenting a set of such model problems. We specifically examine a type of PDE-constrained optimization problem, the parameter estimation problem. We present three model parameter estimation problems, each containing a different type of partial differential equation as the constraint. We also shortly describe discretization and solution techniques for each problem. We further supply a simple to modify matlab code with the article.