Differentiability properties of the L 1 -tracking functional and application to the Robin inverse problem

DOI10.1088/0266-5611/20/4/006zbMath1061.35163OpenAlexW2081585768MaRDI QIDQ4832305

Slim Chaabane, Karl Kunisch, Jamel Ferchichi

Publication date: 4 January 2005

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0266-5611/20/4/006

zbMATH Keywords

cost functionaloptimization problemidentifiabilityexistence of an optimal controlRobin parameterNewton differentiability

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Inverse problems for PDEs (35R30) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (17)

Quadratic convergence of Levenberg-Marquardt method for elliptic and parabolic inverse robin problems ⋮ Differentiability of the objective in a class of coefficient inverse problems ⋮ Pointwise inequalities of logarithmic type in Hardy-Hölder spaces ⋮ Numerical identification of Robin coefficient by a Kohn–Vogelius type regularization method ⋮ BDF2 schemes for optimal parameter control problems governed by bilinear parabolic equations ⋮ Analysis of an Adaptive Finite Element Method for Recovering the Robin Coefficient ⋮ Identification of piecewise constant Robin coefficient for the Stokes problem using the Levenberg-Marquardt method ⋮ Unnamed Item ⋮ A numerical estimation of the piecewise constant Robin coefficient by identifying its discontinuous points ⋮ Solving a nonlinear inverse Robin problem through a linear Cauchy problem ⋮ A primal-dual approach for the Robin inverse problem in a nonlinear elliptic equation: the case of the \(L^1 - L^2\) cost functional ⋮ Global Uniqueness and Lipschitz-Stability for the Inverse Robin Transmission Problem ⋮ Inversion of Robin coefficient by a spectral stochastic finite element approach ⋮ Conjugate Gradient Method for Estimation of Robin Coefficients ⋮ Estimation of the Robin coefficient field in a Poisson problem with uncertain conductivity field ⋮ Uniqueness results for inverse Robin problems with bounded coefficient ⋮ Estimates in the Hardy-Sobolev space of the annulus and stability result

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