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Nonmonotone Levenberg–Marquardt Algorithms and Their Convergence Analysis

Author

Listed:
  • J. Z. Zhang

    (City University of Hong Kong)

  • L. H. Chen

    (Beijing University of Science and Technology)

Abstract

In this paper, two nonmonotone Levenberg–Marquardt algorithms for unconstrained nonlinear least-square problems with zero or small residual are presented. These algorithms allow the sequence of objective function values to be nonmonotone, which accelerates the iteration progress, especially in the case where the objective function is ill-conditioned. Some global convergence properties of the proposed algorithms are proved under mild conditions which exclude the requirement for the positive definiteness of the approximate Hessian T(x). Some stronger global convergence properties and the local superlinear convergence of the first algorithm are also proved. Finally, a set of numerical results is reported which shows that the proposed algorithms are promising and superior to the monotone Levenberg–Marquardt algorithm according to the numbers of gradient and function evaluations.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:92:y:1997:i:2:d:10.1023_a:1022615415582
    DOI: 10.1023/A:1022615415582
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    Cited by:

    1. 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.

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