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A unified local convergence analysis of inexact constrained Levenberg–Marquardt methods

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Abstract

The Levenberg–Marquardt method is a regularized Gauss–Newton method for solving systems of nonlinear equations. If an error bound condition holds it is known that local quadratic convergence to a non-isolated solution can be achieved. This result was extended to constrained Levenberg–Marquardt methods for solving systems of equations subject to convex constraints. This paper presents a local convergence analysis for an inexact version of a constrained Levenberg–Marquardt method. It is shown that the best results known for the unconstrained case also hold for the constrained Levenberg–Marquardt method. Moreover, the influence of the regularization parameter on the level of inexactness and the convergence rate is described. The paper improves and unifies several existing results on the local convergence of Levenberg–Marquardt methods.

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Authors and Affiliations

  1. Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, RJ, 22460-320, Brazil

    Roger Behling

  2. Department of Mathematics, Institute of Numerical Mathematics, Technische Universität Dresden, 01062, Dresden, Germany

    Andreas Fischer

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  1. Roger Behling
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  2. Andreas Fischer
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Correspondence to Andreas Fischer.

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Behling, R., Fischer, A. A unified local convergence analysis of inexact constrained Levenberg–Marquardt methods. Optim Lett 6, 927–940 (2012). https://doi.org/10.1007/s11590-011-0321-3

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  • DOI: https://doi.org/10.1007/s11590-011-0321-3

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