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Perturbation Lemma for the Newton Method with Application to the SQP Newton Method

Author

Listed:
  • D. Cores

    (INTEVEP, Research Center of the Venezuelan Oil Company)

  • R. A. Tapia

    (Rice University)

Abstract

We study the convergence of a general perturbation of the Newton method for solving a nonlinear system of equations. As an application, we show that the augmented Lagrangian successive quadratic programming is locally and q-quadratically convergent in the variable x to the solution of an equality constrained optimization problem, under a mild condition on the penalty parameter and the choice of the Lagrange multipliers.

Suggested Citation

  • D. Cores & R. A. Tapia, 1998. "Perturbation Lemma for the Newton Method with Application to the SQP Newton Method," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 271-280, May.
    • Handle: RePEc:spr:joptap:v:97:y:1998:i:2:d:10.1023_a:1022622532499
    DOI: 10.1023/A:1022622532499
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    Cited by:

    1. E. Cătinaş, 2001. "Inexact Perturbed Newton Methods and Applications to a Class of Krylov Solvers," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 543-570, March.

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