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Global Convergence Technique for the Newton Method with Periodic Hessian Evaluation

Author

Listed:
  • F. Lampariello

    (National Research Council)

  • M. Sciandrone

    (National Research Council)

Abstract

The problem of globalizing the Newton method when the actual Hessian matrix is not used at every iteration is considered. A stabilization technique is studied that employs a new line search strategy for ensuring the global convergence under mild assumptions. Moreover, an implementable algorithmic scheme is proposed, where the evaluation of the second derivatives is conditioned to the behavior of the algorithm during the minimization process and the local convexity properties of the objective function. This is done in order to obtain a significant computational saving, while keeping acceptable the unavoidable degradation in convergence speed. The numerical results reported indicate that the method described may be employed advantageously in all applications where the computation of the Hessian matrix is highly time consuming.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:2:d:10.1023_a:1011934418390
    DOI: 10.1023/A:1011934418390
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    Cited by:

    1. Bilel Kchouk & Jean-Pierre Dussault, 2013. "The Chebyshev–Shamanskii Method for Solving Systems of Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 157(1), pages 148-167, April.
    2. 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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