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Preface: Optimal control and inverse problems. (English) Zbl 1435.00059

The papers collected in this special issue present topics at the current forefront of researchin optimal control of differential equations and illustrate their relation to inverse problems.

MSC:

00B15 Collections of articles of miscellaneous specific interest
90-06 Proceedings, conferences, collections, etc. pertaining to operations research and mathematical programming
35-06 Proceedings, conferences, collections, etc. pertaining to partial differential equations
49-06 Proceedings, conferences, collections, etc. pertaining to calculus of variations and optimal control
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References:

[1] Tröltzsch F 2010 Optimal Control of Partial Differential Equations(Graduate Studies in Mathematics vol 112) (Providence, RI: American Mathematical Society)
[2] Hinze M, Pinnau R, Ulbrich M and Ulbrich S 2009 Optimization with PDE Constraints (Berlin: Springer) · Zbl 1167.49001
[3] De los Reyes J C 2015 Numerical PDE-Constrained Optimization (Berlin: Springer) · Zbl 1312.65100
[4] Casas E and Kunisch K 2019 Using sparse control methods to identify sources in linear diffusion-convection equations Inverse Problems35 114002 · Zbl 1447.35376
[5] Bergmann R, Herrmann M, Herzog R, Schmidt S and Vidal Núñez J 2020 Total variation of the normal vector field as shape prior Inverse Problems accepted manuscript
[6] Bergmann R, Herrmann M, Herzog R, Schmidt S and Vidal Núñez J 2020 Discrete total variation of the normal vector field as shape prior with applications in geometric inverse problems Inverse Problems36 054003
[7] Hinze M and Tam Quyen T N 2019 Finite element approximation of source term identification with TV-regularization Inverse Problems35 124004 · Zbl 1427.65344
[8] Jin B and Xu Y 2020 Adaptive reconstruction for electrical impedance tomography with a piecewise constant conductivity Inverse Problems36 014003 · Zbl 1439.35564
[9] Migórski S, Khan A A and Zeng S 2020 Inverse problems for nonlinear quasi-hemivariational inequalities with application to mixed boundary value problems Inverse Problems36 024006 · Zbl 1433.35462
[10] Antil H, Khatri R and Warma M 2019 External optimal control of nonlocal PDEs Inverse Problems35 084003 · Zbl 1461.35221
[11] Hiles A J and Oliver D 2020 Sparsity and level set regularization for near-field electromagnetic imaging in 3D Inverse Problems36 025012 · Zbl 1433.78033
[12] Bergounioux M, Bretin É and Privat Y 2019 How to position sensors in thermo-acoustic tomography Inverse Problems35 074003 · Zbl 1418.92068
[13] Haubner J, Ulbrich M and Ulbrich S 2020 Analysis of shape optimization problems for unsteady fluid-structure interaction Inverse Problems36 034001 · Zbl 1440.49044
[14] Gaspoz F, Kreuzer C, Veeser A and Wollner W 2020 Quasi-best approximation in optimization with PDE constraints Inverse Problems36 014004 · Zbl 1457.49022
[15] Beigl A, Scherzer O, Sogn J and Zulehner W 2020 Preconditioning inverse problems for hyperbolic equations with applications to photoacoustic tomography Inverse Problems36 014002 · Zbl 1485.65064
[16] Gong R, Hofmann B and Zhang Y 2020 A new class of accelerated regularization methods, with application to bioluminescence tomography Inverse Problems accepted manuscript
[17] Jadamba B, Khan A A, Richards M and Sama M 2020 A convex inversion framework for identifying parameters in saddle point problems with applications to inverse incompressible elasticity Inverse Problems (accepted)
[18] Burger M, Pietschmann J-F and Wolfram M-T 2020 Data assimilation in price formation Inverse Problems accepted manuscript
[19] Liu J and Xiao M 2019 Quasi-boundary value methods for regularizing the backward parabolic equation under the optimal control framework Inverse Problems35 124003 · Zbl 1425.35235
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