A Class of Factorized Quasi-Newton Methods for Nonlinear Least Squares Problems

Abstract

This paper gives a class of descent methods for nonlinear least squares solution. A class of updating formulae is obtained by using generalized inverse matrices. These formulae generate an approximation to the second part of the Hessian matrix of the objective function, and are updated in such a way that the resulting approximation to the whole Hessian matrix is the convex class of Broyden-like updating formulae. It is proved that the proposed updating formulae are invariant under linear transformation and that the class of factorized quasi-Newton methods are locally and superlinearly convergent. Numerical results are presented and show that the proposed methods are promising.