Local convergence analysis for partitioned quasi-Newton updates

Andreas Griewank, Philippe Toint

    Research output: Contribution to journalArticlepeer-review


    This paper considers local convergence properties of inexact partitioned quasi-Newton algorithms for the solution of certain non-linear equations and, in particular, the optimization of partially separable objective functions. Using the bounded deterioration principle, one obtains local and linear convergence, which implies Q-superlinear convergence under the usual conditions on the quasi-Newton updates. For the optimization case, these conditions are shown to be satisfied by any sequence of updates within the convex Broyden class, even if some Hessians are singular at the minimizer. Finally, local and Q-superlinear convergence is established for an inexact partitioned variable metric method under mild assumptions on the initial Hessian approximations. © 1982 Springer-Verlag.
    Original languageEnglish
    Pages (from-to)429-448
    Number of pages20
    JournalNumerische Mathematik
    Publication statusPublished - 1 Oct 1982


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