Optimization applications arising from discretized continuous problems are large, important and numerous (think of PDE or optimal control problems or weather forecast, for instance). For such applications, it seems natural to exploit, when possible, the knowledge of the problem description on a hierarchy of fine to coarse meshes to speed up the optimization algorithm (as is typically done in multigrid methods to solve systems of equations, yielding solvers with linear complexity in problem size). However, it is also of particular importance, in a nonlinear optimization context, to ensure a globally convergent process, as do classical line search or trust region based optimization algorithms.
We will outline some possible ways of efficiently adapting globalization techniques to multi-scale optimization. We will also discuss some theoretical and practical aspects and present some numerical experimentations.
Annick Sartenaer, Universite Notre Dame de la Paix, Belgium