Algorithmic Differentiation and Nonlinear Optimization for an Inverse Medium Problem and Andreas Wa¨chter
Numerical optimization, e.g., for the solution of inverse problems for systems described by partial-differential equations (PDEs), is an important aspect of scientific computing. Using the example of an inverse medium problem (Section 8.2), we demonstrate how combinatorial techniques play a significant role for the efficient solution of large-scale optimization problems. In particular, the fast computation of sparse derivative matrices using algorithmic
differentiation (Section 8.5) is made possible by coloring algorithms, and the efficient solution of sparse linear systems (Section 8.6) requires weighted graph matching algorithms.