Numerische Mathematik

, Volume 39, Issue 3, pp 429–448

Local convergence analysis for partitioned quasi-Newton updates

  • A. Griewank
  • Ph. L. Toint
Error Estimation in Coefficients of Exponential Sums and Polynomials

DOI: 10.1007/BF01407874

Cite this article as:
Griewank, A. & Toint, P.L. Numer. Math. (1982) 39: 429. doi:10.1007/BF01407874

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.

Subject Classifications

AMS(MOS): 65K05 CR: 5.15 

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • A. Griewank
    • 1
    • 2
  • Ph. L. Toint
    • 1
    • 2
  1. 1.Department of Southern Mathematics Methodist UniversityDallasUSA
  2. 2.Department of MathematicsFacultes Universitaires de NamurNamurBelgium

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