Global convergence of quasi-Newton methods based on adjoint Broyden updates

In this paper we introduce a quasi-Newton method for the solution of systems of non-linear equations based on the nested application of adjoint Broyden updates. In combination with a suitable line search this method yields convergence of the iteration under the same requirements on F as Newtonʹs method. The successive use of adjoint Broyden updates yields even local r-linear convergence of the iteration and provides the requirements for the local convergence analysis that gives q-superlinear convergence of the iteration.