Stable factorized quasi-Newton methods for nonlinear least-squares problems

In this paper, we consider stable factorized quasi-Newton methods for solving nonlinear least-squares problems. Based on the QR decomposition of the Jacobian of the residual function, updating a rectangular correction matrix to the Jacobian is changed to updating a square matrix of lower order. A new class of factorized quasi-Newton methods is proposed. It is proved that this type of methods possesses locally superlinear convergence property under mild conditions. Numerical results compared with the original algorithms are presented.