Adjoint-based optimization of PDE systems with alternative gradients

In this work we investigate a technique for accelerating convergence of adjoint-based optimization of PDE systems based on a nonlinear change of variables in the control space. This change of variables is accomplished in the “differentiate – then – discretize” approach by constructing the descent directions in a control space not equipped with the Hilbert structure. We show how such descent directions can be computed in general Lebesgue and …