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Structured Two-Point Stepsize Gradient Methods for Nonlinear Least Squares

Author

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  • Hassan Mohammad

    (Bayero University
    University of Campinas)

  • Mohammed Yusuf Waziri

    (Bayero University)

Abstract

In this paper, we present two choices of structured spectral gradient methods for solving nonlinear least squares problems. In the proposed methods, the scalar multiple of identity approximation of the Hessian inverse is obtained by imposing the structured quasi-Newton condition. Moreover, we propose a simple strategy for choosing the structured scalar in the case of negative curvature direction. Using the nonmonotone line search with the quadratic interpolation backtracking technique, we prove that these proposed methods are globally convergent under suitable conditions. Numerical experiment shows that the methods are competitive with some recently developed methods.

Suggested Citation

  • Hassan Mohammad & Mohammed Yusuf Waziri, 2019. "Structured Two-Point Stepsize Gradient Methods for Nonlinear Least Squares," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 298-317, April.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:1:d:10.1007_s10957-018-1434-y
    DOI: 10.1007/s10957-018-1434-y
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    References listed on IDEAS

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    1. Wei Xu & Thomas Coleman & Gang Liu, 2012. "A secant method for nonlinear least-squares minimization," Computational Optimization and Applications, Springer, vol. 51(1), pages 159-173, January.
    2. J. Z. Zhang & N. Y. Deng & L. H. Chen, 1999. "New Quasi-Newton Equation and Related Methods for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 147-167, July.
    3. Fahimeh Biglari & Maghsud Solimanpur, 2013. "Scaling on the Spectral Gradient Method," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 626-635, August.
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    Cited by:

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