Title: Parameter estimation with the augmented Lagrangian method for a parabolic equation

Author: Trygve K. Nilssen and Xue--Cheng Tai

Abstract:
In this paper, we investigate the numerical identification of the diffusion 
parameters in parabolic problems. 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 method, even for identifying highly 
discontinuous parameters.