Convergence Rate of the Augmented Lagrangian SQP Method |
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Authors: | D Kleis E W Sachs |
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Institution: | (1) Fachbereich IV-Mathematik, Universität Trier, Trier, Germany;(2) Fachbereich IV-Mathematik and Graduiertenkolleg Mathematische Optimierung, Universität Trier, Trier, Germany |
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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, ). 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. |
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Keywords: | SQP methods infinite-dimensional optimization convergence rate parameter identification |
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