Convergence of a Factorized Broyden-Like Family for Nonlinear Least Squares Problems

This paper is concerned with factorized quasi-Newton methods for nonlinear least squares problems. A one parameter class of symmetric positive definite quasi-Newton updates is given that corresponds to the Broyden family. We call this new class of update formula a factorized Broyden-like family. This family is based on the full rank factorized form of a structured quasi-Newton update. We prove that a quasi-Newton method using the factorized Broyden-like family possesses local and q-superlinear convergence properties.