Convergence Rate of the Augmented Lagrangian SQP Method

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 neces...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 95; no. 1; pp. 49 - 74
Main Authors: Kleis, D., Sachs, E. W.
Format: Journal Article
Language:English
Published: New York, NY Springer 01.10.1997
Springer Nature B.V
Subjects:
Applied sciences
Building materials. Ceramics. Glasses
Ceramic industries
Chemical industry and chemicals
Computer science; control theory; systems
Control theory. Systems
Exact sciences and technology
Miscellaneous
Optimal control
Parameter identification
Parameter estimation
Sequential method
Optimal control
Non linear model
Convergence rate
Ceramics industry
Infinite dimension
Diffusion
Quadratic programming
Algorithm
Lagrangian method
Newton method
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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.
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ISSN:0022-3239
1573-2878
DOI:10.1023/A:1022631327800