Abstract
This paper presents a local convergence analysis of Broyden's class of rank-2 algorithms for solving unconstrained minimization problems,\(h(\bar x) = \min h(x)\),h ∈ C1(R n), assuming that the step-size ai in each iterationx i+1 =x i -α i H i ▽h(x i ) is determined by approximate line searches only. Many of these methods including the ones most often used in practice, converge locally at least with R-order,\(\tau \geqslant \sqrt[n]{2}\).
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Stoer, J. On the convergence rate of imperfect minimization algorithms in Broyden'sβ-class. Mathematical Programming 9, 313–335 (1975). https://doi.org/10.1007/BF01681353
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DOI: https://doi.org/10.1007/BF01681353