Many large nonlinear optimization problems are based upon discretizations of underlying function spaces. Optimization-based multigrid methods—that is, multigrid methods based on solving coarser versions of an optimization problem—are designed to solve such discretized problems efficiently by taking explicit advantage of the family of discretizations. The methods are generalizations of more traditional multigrid methods for solving partial differential equations. These multigrid methods are a powerful tool, but they are not appropriate for all optimization problems. We discuss techniques whereby the multigrid method can assess the properties of the optimization problem, with the goal of automatically determining whether the optimization problem is well suited for the multigrid-type algorithm.
Citation
http://www.math.wm.edu/~buckaroo/pubs/LeNa08a.pdf, Technical Report, College of William & Mary, 2008