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A Truncated Nonmonotone Gauss-Newton Method for Large-Scale Nonlinear Least-Squares Problems

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Abstract

In this paper, a Gauss-Newton method is proposed for the solution of large-scale nonlinear least-squares problems, by introducing a truncation strategy in the method presented in [9]. First, sufficient conditions are established for ensuring the convergence of an iterative method employing a truncation scheme for computing the search direction, as approximate solution of a Gauss-Newton type equation. Then, a specific truncated Gauss-Newton algorithm is described, whose global convergence is ensured under standard assumptions, together with the superlinear convergence rate in the zero-residual case. The results of a computational experimentation on a set of standard test problems are reported.

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Authors and Affiliations

  1. Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti” - CNR, Viale Manzoni 30, 00185, Roma, Italy

    G. Fasano, F. Lampariello & M. Sciandrone

  2. Istituto Nazionale per Studi ed Esperienze di Architettura Navale INSEAN, Via di Vallerano 139, 00128, Roma, Italy

    G. Fasano

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  1. G. Fasano
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  2. F. Lampariello
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  3. M. Sciandrone
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Correspondence to G. Fasano.

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Fasano, G., Lampariello, F. & Sciandrone, M. A Truncated Nonmonotone Gauss-Newton Method for Large-Scale Nonlinear Least-Squares Problems. Comput Optim Applic 34, 343–358 (2006). https://doi.org/10.1007/s10589-006-6444-2

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  • DOI: https://doi.org/10.1007/s10589-006-6444-2

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