Project : tropics
Section: New Results
Keywords : optimization, multilevel, gradient, reduced models.
Multilevel optimization and reduced models
As stated in 6.5, the very large numebr of parameters of interest for optimal control problems using the adjoint approach comes from the discretization of a functional parametrization. Not only do we have to take into account the number of parameters, but we should take some benefit from the information we can get about the functional parametrization. This can help designing an efficient functional preconditioner. In contrast to algebraic ones, ``functional preconditioners'' are not derived from the operator to precondition by some algebraic transformation. They are derived from an analysis of the functional context at the origin of the discrete problem. The functional preconditioner we have built for shape design application is an additive multilevel preconditioner. The multilevel basis was also applied in cooperation with project-team Smash to the derivation of reduced models that can be introduced in sophisticated optimizers. .