A Globally Convergent Algorithm for a PDE-Constrained Optimization Problem Arising in Electrical Impedance Tomography

DOI10.1080/01630563.2015.1031379zbMath1319.65050OpenAlexW1984320402MaRDI QIDQ5264021

Juan Alfredo Gómez, Mauricio Carrillo

Publication date: 20 July 2015

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630563.2015.1031379

zbMATH Keywords

algorithmnumerical exampleglobal convergenceinverse problemfinite element discretizationelliptic equationsleast squares methodelectrical impedance tomographypotential equationWolfe's conditions

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Methods of quasi-Newton type (90C53) Boundary value problems for second-order elliptic equations (35J25) Inverse problems for PDEs (35R30) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Existence theories for optimal control problems involving partial differential equations (49J20) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21)

Cites Work

• Structural stability in a minimization problem and applications to conductivity imaging
• Computational methods in optimization. A unified approach.
• A nonlinear multigrid for imaging electrical conductivity and permittivity at low frequency
• A reconstruction algorithm for electrical impedance tomography based on sparsity regularization
• Algorithms for PDE-constrained optimization
• Handbook of Mathematical Methods in Imaging
• Determining conductivity by boundary measurements
• Convergence of a Reconstruction Method for the Inverse Conductivity Problem
• Global convergence of a multidirectional algorithm for unconstrained optimal control problems
• Regularizing properties of a truncated newton-cg algorithm for nonlinear inverse problems
• Numerical Methods for Elliptic and Parabolic Partial Differential Equations
• First-Order System Least Squares and Electrical Impedance Tomography
• On the Finite Element Solution of the Pure Neumann Problem
• Inverse problems for partial differential equations
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