CONVERGENCE OF A FACTORIZED BROYDEN-LIKE FAMILY FOR NONLINEAR LEAST-SQUARES PROBLEMS

This paper is concerned with factorized quasi-Newton methods for nonli near least squares problems. A one parameter class of symmetric positi ve definite quasi-Newton updates is given that corresponds to the Broy den family. We call this new class of update formula a factorized Broy den-like family. This family is based on the full rank factorized form of a structured quasi-Newton update. We prove that a quasi-Newton met hod using the factorized Broyden-like family possesses local and q-sup erlinear convergence properties.