A note on the equivalence of a class of factorized Broyden families for nonlinear least squares problems

Abstract

This note is concerned with the recently proposed two factorized quasi-Newton updates for solving nonlinear least squares problems. One is a class of updates proposed by Yabe and Yamaki (SIAM Journal on Optimization 5 (1995) 770–791), which was designed as a factorized version of the structured Broyden family with a nonnegative parameter. The other is a class of updates of Xu, Ma and Kong (Journal of Computational Mathematics 14 (1996) 143–158) which was derived as a class of updates satisfying the secant condition in factorized form. It is shown that these classes of updates are essentially the same.