Factorized quasi-Newton methods for nonlinear least squares problems

This paper provides a modification to the Gauss-Newton method for nonlinear least squares problems. The new method is based on structured quasi-Newton methods which yield a good approximation to the second derivative matrix of the objective function. In particular, the authors propose BFGS-like and DFP-like updates in a factorized form which give descent search directions for the objective function. They prove local and q-superlinear convergence of the present methods, and give results of computational experiments for the BFGS-like and DFP-like updates.