On the convergence rate of imperfect minimization algorithms in Broyden'sβ-class

@article{Stoer1975OnTC,
  title={On the convergence rate of imperfect minimization algorithms in Broyden'sβ-class},
  author={Josef Stoer},
  journal={Math. Program.},
  year={1975},
  volume={9},
  pages={313-335}
}
This paper presents a local convergence analysis of Broyden 's class of rank-2 algor i thms for solving unconstrained minimizat ion problems, h(2) = minh(x ) , h ~ CI(Rn), assuming that the step-size c~ i in each iteration xi+ l = x i c~iHiVh(xi) is de termined by approximate line searches only. Many of these me thods including the ones mos t often used in practice, converge locally at least with R-order, r >~ ~ .