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Use of the Minimum-Norm Search Direction in a Nonmonotone Version of the Gauss-Newton Method

Author

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  • F. Lampariello

    (Istituto di Analisi dei Sistemi ed Informatica)

  • M. Sciandrone

    (Istituto di Analisi dei Sistemi ed Informatica)

Abstract

In this work, a new stabilization scheme for the Gauss-Newton method is defined, where the minimum norm solution of the linear least-squares problem is normally taken as search direction and the standard Gauss-Newton equation is suitably modified only at a subsequence of the iterates. Moreover, the stepsize is computed by means of a nonmonotone line search technique. The global convergence of the proposed algorithm model is proved under standard assumptions and the superlinear rate of convergence is ensured for the zero-residual case. A specific implementation algorithm is described, where the use of the pure Gauss-Newton iteration is conditioned to the progress made in the minimization process by controlling the stepsize. The results of a computational experimentation performed on a set of standard test problems are reported.

Suggested Citation

  • F. Lampariello & M. Sciandrone, 2003. "Use of the Minimum-Norm Search Direction in a Nonmonotone Version of the Gauss-Newton Method," Journal of Optimization Theory and Applications, Springer, vol. 119(1), pages 65-82, October.
    • Handle: RePEc:spr:joptap:v:119:y:2003:i:1:d:10.1023_b:jota.0000005041.99777.af
    DOI: 10.1023/B:JOTA.0000005041.99777.af
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    References listed on IDEAS

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    1. F. Lampariello & M. Sciandrone, 2001. "Global Convergence Technique for the Newton Method with Periodic Hessian Evaluation," Journal of Optimization Theory and Applications, Springer, vol. 111(2), pages 341-358, November.
    2. J. Z. Zhang & L. H. Chen, 1997. "Nonmonotone Levenberg–Marquardt Algorithms and Their Convergence Analysis," Journal of Optimization Theory and Applications, Springer, vol. 92(2), pages 393-418, February.
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    Cited by:

    1. G. Fasano, 2007. "Lanczos Conjugate-Gradient Method and Pseudoinverse Computation on Indefinite and Singular Systems," Journal of Optimization Theory and Applications, Springer, vol. 132(2), pages 267-285, February.

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