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Convergence Rate of the Augmented Lagrangian SQP Method

Author

Listed:
  • D. Kleis

    (Universität Trier)

  • E. W. Sachs

    (Universität Trier)

Abstract

In this paper, the augmented Lagrangian SQP method is considered for the numerical solution of optimization problems with equality constraints. The problem is formulated in a Hilbert space setting. Since the augmented Lagrangian SQP method is a type of Newton method for the nonlinear system of necessary optimality conditions, it is conceivable that q-quadratic convergence can be shown to hold locally in the pair (x, λ). Our interest lies in the convergence of the variable x alone. We improve convergence estimates for the Newton multiplier update which does not satisfy the same convergence properties in x as for example the least-square multiplier update. We discuss these updates in the context of parameter identification problems. Furthermore, we extend the convergence results to inexact augmented Lagrangian methods. Numerical results for a control problem are also presented.

Suggested Citation

  • D. Kleis & E. W. Sachs, 1997. "Convergence Rate of the Augmented Lagrangian SQP Method," Journal of Optimization Theory and Applications, Springer, vol. 95(1), pages 49-74, October.
    • Handle: RePEc:spr:joptap:v:95:y:1997:i:1:d:10.1023_a:1022631327800
    DOI: 10.1023/A:1022631327800
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