Application of Targeted Automatic Differentiation to Large-Scale Dynamic Optimization

Abstract

A targeted AD approach is presented to calculate directional second order derivatives of ODE/DAE embedded functionals accurately and efficiently. This advance enables us to tackle the solution of large scale dynamic optimization problems using a truncated-Newton method where the Newton equation is solved approximately to update the direction for the next optimization step. The proposed directional second order adjoint method (dSOA) provides accurate Hessian-vector products for this algorithm. The implementation of the "dSOA powered" truncated-Newton method for the solution of large scale dynamic optimization problems is showcased with an example.