Inverse Optical Tomography through PDE Constrained Optimization $L^\infty$
DOI10.1137/19M1239908zbMath1430.49037arXiv1812.10319MaRDI QIDQ5207032
Publication date: 19 December 2019
Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1812.10319
Lagrange multipliersRobin boundary conditionselliptic systemsabsolute minimizersPDE-constrained optimizationnonlinear inversionKuhn-Tucker theorycalculus of variations in \(L^{\infty}\)fluorescent optical tomography
Optimality conditions for problems involving partial differential equations (49K20) Variational and other types of inequalities involving nonlinear operators (general) (47J20) Variational inequalities (49J40) Fréchet and Gateaux differentiability in optimization (49J50) Biomedical imaging and signal processing (92C55) Inverse problems in optimal control (49N45) Variational principles of physics (49S05)
Related Items (4)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- \(L ^{\infty }\) variational problems with running costs and constraints
- Uniqueness of absolute minimizers for \(L^\infty\)-functionals involving Hamiltonians \(H(x,p)\)
- Regularity of solutions of linear second order elliptic and parabolic boundary value problems on Lipschitz domains
- \(W^{1,p}\) estimates for elliptic problems with Neumann boundary conditions in Lipschitz domains
- On certain minimax problems and Pontryagin's maximum principle
- On the lower semicontinuity and approximation of \(L^\infty\)-functionals
- Elliptic equations in divergence form with partially BMO coefficients
- Elliptic partial differential equations of second order
- The eigenvalue problem for the \(\infty \)-Bilaplacian
- Existence, uniqueness and structure of second order absolute minimisers
- Uniform \(W^{1,p}\) estimates for an elliptic operator with Robin boundary condition in a \(\mathcal{C}^1\) domain
- Second-order \(L^\infty\) variational problems and the \(\infty\)-polylaplacian
- Minimization problems for the functional \(\displaystyle{\sup_x}\, F(x,f(x),f'(x))\). I, II
- Extension of functions satisfying Lipschitz conditions
- An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs
- An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L∞
- Adaptive finite element methods for the solution of inverse problems in optical tomography
- $\Gamma$-Convergence of Power-Law Functionals, Variational Principles in $L^{\infty},$ and Applications
- Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
- Optical tomography in medical imaging
- Robin boundary value problems on arbitrary domains
- Dielectric breakdown: optimal bounds
- Viscosity solutions of stationary Hamilton-Jacobi equations and minimizers of $L^{\infty }$ functionals
- An $L^\infty$ Regularization Strategy to the Inverse Source Identification Problem for Elliptic Equations
- A Lie symmetry analysis and explicit solutions of the two‐dimensional ∞‐Polylaplacian
- A minimisation problem in L∞ with PDE and unilateral constraints
- Existence of Minimizers for NonLevel Convex Supremal Functionals
- Homogenization of elliptic systems with Neumann boundary conditions
- Γ-convergence and absolute minimizers for supremal functionals
- Optical tomography as a PDE-constrained optimization problem
- Minimizing theL∞Norm of the Gradient with an Energy Constraint
- Direct methods in the calculus of variations
- The Euler equation and absolute minimizers of \(L^\infty\) functionals
This page was built for publication: Inverse Optical Tomography through PDE Constrained Optimization $L^\infty$
