Parameter Estimation with the Augmented Lagrangian Method for a Parabolic Equation

T. K. Nilssen and X. C. Tai
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T. K. Nilssen: Simula Research Laboratory
X. C. Tai: University of Bergen

Journal of Optimization Theory and Applications, 2005, vol. 124, issue 2, No 9, 435-453

Abstract: Abstract In this paper, we investigate the numerical identification of the diffusion parameters in a linear parabolic problem. The identification is formulated as a constrained minimization problem. By using the augmented Lagrangian method, the inverse problem is reduced to a coupled nonlinear algebraic system, which can be solved efficiently with the preconditioned conjugate gradient method. Finally, we present some numerical experiments to show the efficiency of the proposed methods, even for identifying highly discontinuous parameters.

Keywords: Parameter estimation; inverse problems; parabolic equations; augmented Lagrangian methods; conjugate gradient methods (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1007/s10957-004-0944-y

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