Factorized quasi-Newton methods for nonlinear least squares problems (Q1176806)

This method provides a modification of 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, we propose BFGS-like and DFP-like updates in a factorized form which give descent search directions for the objective function. We prove local and \(q\)- superliner convergence of our methods, and give results of computational experiments for the BFGS-like and DFP-like updates.