Parameter estimation with the augmented Lagrangian method for a parabolic equation

DOI10.1007/s10957-004-0944-yzbMath1062.49028OpenAlexW2017956962MaRDI QIDQ1777597

Niranjan Chakravarthy

Publication date: 24 May 2005

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1956/19541

zbMATH Keywords

parameter estimationinverse problemsparabolic equationsconjugate gradient methodsaugmented Lagrangian methods

Mathematics Subject Classification ID

Optimal feedback synthesis (49N35) System identification (93B30) Inverse problems for PDEs (35R30) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32)

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Retrieving the variable coefficient for a nonlinear convection–diffusion problem with spectral conjugate gradient method ⋮ A wavelet multiscale method for the inverse problem of a nonlinear convection-diffusion equation ⋮ A piecewise constant level set method for elliptic inverse problems ⋮ BDF2 schemes for optimal parameter control problems governed by bilinear parabolic equations ⋮ Numerical approximation of the optimal control of a population dynamics model ⋮ Application of regularization technique to variational adjoint method: A case for nonlinear convection-diffusion problem ⋮ An efficient numerical parameter estimation scheme for the space-dependent dispersion coefficient of a solute transport equation in porous media ⋮ Numerical Study of Inverse Source Problem for Internal Degenerate Parabolic Equation ⋮ Identification of diffusion parameters in a nonlinear convection-diffusion equation using the augmented Lagrangian method ⋮ Identification of space-dependent permeability in nonlinear diffusion equation from interior measurements using wavelet multiscale method ⋮ Numerical Estimation of a Diffusion Coefficient in Subdiffusion ⋮ An adaptive homotopy method for permeability estimation of a nonlinear diffusion equation

Cites Work

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• Estimation of a temporally and spatially varying diffusion coefficient in a parabolic system by an augmented Lagrangian technique
• Error estimates for distributed parameter identification in parabolic problems with output least squares and Crank-Nicolson method
• An Efficient Linear Solver for Nonlinear Parameter Identification Problems
• Sequential and Parallel Splitting Methods for Bilinear Control Problems in Hilbert Spaces
• The Augmented Lagrangian Method for Parameter Estimation in Elliptic Systems
• An Augmented Lagrangian Method for Identifying Discontinuous Parameters in Elliptic Systems
• Numerical identifications of parameters in parabolic systems
• Identification of Discontinuous Coefficients in Elliptic Problems Using Total Variation Regularization
• A new approach to convergence rate analysis of Tikhonov regularization for parameter identification in heat conduction
• An augmented Lagrangian method for parameter identifications in parabolic systems

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