Levenberg Marquardt Algorithms for Nonlinear Least Squares Minimization for Solving Inverse Problems

Levenberg Marquardt (LM) algorithms are a class of methods that add a regularization term to a Gauss Newton iteration to promote better convergence properties. This talk presents three works on this class of methods. The first discusses a new LM algorithm that simultaneously achieves all of state of the art convergence guarantees for unconstrained problems. Stochastic LM is discussed next, which is an algorithm to handle noisy data. Convergence is proven with respect to an expected stopping time for approximate stationarity. Finally, a LM method is presented to handle nonlinear equality constraints, with numerical examples from large scale inverse problems in PDEs.