Convergence Rate of the Augmented Lagrangian SQP Method

D. Kleis and E. W. Sachs
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D. Kleis: Universität Trier
E. W. Sachs: Universität Trier

Journal of Optimization Theory and Applications, 1997, vol. 95, issue 1, No 3, 49-74

Abstract: 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.

Keywords: SQP methods; infinite-dimensional optimization; convergence rate; parameter identification (search for similar items in EconPapers)
Date: 1997
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DOI: 10.1023/A:1022631327800

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