Summary
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 impliesQ-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 andQ-superlinear convergence is established for an inexact partitioned variable metric method under mild assumptions on the initial Hessian approximations.
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Work supported by a research grant of the Deutsche Forschungsgemeinschaft, Bonn and carried out at the Department of Applied Mathematics and Theoretical Physics Cambridge (United Kingdom)
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Griewank, A., Toint, P.L. Local convergence analysis for partitioned quasi-Newton updates. Numer. Math. 39, 429–448 (1982). https://doi.org/10.1007/BF01407874
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DOI: https://doi.org/10.1007/BF01407874