Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations

We present a multigrid approach to the optimization of systems governed by differential equations. Such optimization problems have many applications, and are a broader class of problems than systems of equations. Using several model problems we give evidence (both theoretical and numerical) that a multigrid approach can often be successful in the setting of optimization. One of the model problems shows that the approach is applicable to the optimization problem even though multigrid applied directly to the solution of the governing differential equation might not be appropriate or effective. In addition, we relate the multigrid approach to more traditional optimization algorithms, as further justification for the application of multigrid to optimization problems.


SIAM Journal on Scientific Computing, vol. 26 (2005), pp. 1811–1837.