Adjoint based quasi Newton methods for nonlinear equations

In this thesis a new class of rank-1 update formulas is investigated. It is applied to approximate Jacobians in quasi-Newton methods for the solution of nonlinear equations. The update formulas make explicite use of adjoint and partly direct derivative information. For example, these derivatives can be efficiently evaluated by methods of Automatic Differentiation. A particular feature of the update formulas is that they combine the fixed scale least change property of Broyden’s update with the heredity property of the SR1 update. This allows to prove rapid local superlinear convergence. Moreover, in combination with line search, global convergence results are established. The new quasi-Newton methods are applied to various test problems and compared to other well established methods.