Quasi-Newton methods for large-scale electromagnetic inverse problems

Abstract

We develop quasi-Newton (QN) methods for distributed parameter estimation problems which evolve from electromagnetics, where the forward problem is governed by some form of Maxwell's equations. A Tikhonov-style regularization approach yields an optimization problem with a special structure, where the gradients are calculated using the adjoint method. In many cases, standard QN methods (such as L-BFGS) are not very effective and tend to converge slowly. Taking advantage of the special structure of the problem and the quantities that are calculated in typical gradient descent methods, we develop a class of highly effective methods for the solution of the problem. We demonstrate the merits and effectiveness of our algorithm on two realistic model problems.