Singularly Perturbed Markov Decision Processes: A Multiresolution Algorithm

Singular perturbation techniques allow the derivation of an aggregate model whose solution is asymptotically optimal for Markov Decision Processes with strong and weak interactions. We develop an algorithm that takes advantage of the asymptotic optimality of the aggregate model in order to compute the solution of the original model with theoretically better complexity than conventional … Read more

Automatically Assessing the Performance of an Optimization-Based Multigrid Method

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 … Read more

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. … Read more