Andreas Fischer
Institute of Numerical Mathematics, TU Dresden, Germany

Levenberg-Marquardt methods
The Levenberg-Marquardt (LM) method is a regularized Gauss-Newton method. A survey on the recent use of LM methods for equations with nonisolated solutions will be presented. We first focus on the question how the regularization parameter and the level of inexactness in the subproblems influence the local convergence rate. Since an error bound condition is a key assumption for the local fast convergence of LM methods this assumption is discussed in more detail for some applications, e.g., Nash equilibrium problems and multiobjective optimization. Extensions to constrained equations are highlighted as well.