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Optimization Methods and Software Volume 9, 1998 - Issue 4
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Original Articles

Reverse aumulation and imploicit functions

Bruce Christianson Faculty of Information science, University of Hertfordshire, Hatfield, Europe, England E-mail: [email protected]
Pages 307-322 | Received 31 Jul 1996, Published online: 29 Mar 2007

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Bradley M. Bell & Kasper Kristensen. (2018) Newton step methods for AD of an objective defined using implicit functions. Optimization Methods and Software 33:4-6, pages 907-923.
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Torsten Bosse. (2016) Augmenting the one-shot framework by additional constraints. Optimization Methods and Software 31:6, pages 1132-1148.
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Marina Menshikova & Shaun A. Forth. (2012) Automatic differentiation of quadrature. Optimization Methods and Software 27:2, pages 323-335.
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Bruce Christianson. (2001) A self-stabilizing Pantoja-like indirect algorithm for optimal control. Optimization Methods and Software 16:1-4, pages 131-149.
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Bruce Christianson. (1999) Cheap Newton steps for optimal control problems: automatic differentiation and Pantoja's algorithm. Optimization Methods and Software 10:5, pages 729-743.
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Luca Capriotti, Yupeng Jiang & Andrea Macrina. (2016) Real-time risk management: An AAD-PDE approach. International Journal of Financial Engineering 02:04, pages 1550039.
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Shenren Xu, David Radford, Marcus Meyer & Jens-Dominik Müller. (2015) Stabilisation of discrete steady adjoint solvers. Journal of Computational Physics 299, pages 175-195.
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Yang Wang, Siamak Akbarzadeh & Jens D. Mueller. (2015) Stabilisation of Discrete Adjoint Solvers for Incompressible Flow. Stabilisation of Discrete Adjoint Solvers for Incompressible Flow.
Bijan Mohammadi. (2014) Uncertainty quantification by geometric characterization of sensitivity spaces. Computer Methods in Applied Mechanics and Engineering 280, pages 197-221.
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Bijan Mohammadi. (2014) Principal angles between subspaces and reduced order modelling accuracy in optimization. Structural and Multidisciplinary Optimization 50:2, pages 237-252.
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Thomas Slawig, Malte Prieß & Claudia Kratzenstein. 2014. Solving Computationally Expensive Engineering Problems. Solving Computationally Expensive Engineering Problems 1 24 .
Marc Henrard. (2013) Calibration in Finance: Very Fast Greeks Through Algorithmic Differentiation and Implicit Function. Procedia Computer Science 18, pages 1145-1154.
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John Michael Nahay. (2012) The nth Order Implicit Differentiation Formula for Two Variables with an Application to Computing All Roots of a Transcendental Function. Mathematics in Computer Science 6:1, pages 79-105.
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Nicolas Gauger, Andreas Griewank, Adel Hamdi, Claudia Kratzenstein, Emre Özkaya & Thomas Slawig. 2012. Constrained Optimization and Optimal Control for Partial Differential Equations. Constrained Optimization and Optimal Control for Partial Differential Equations 99 122 .
Faidon Christakopoulos, Dominic Jones & Jens-Dominik Müller. (2011) Pseudo-timestepping and verification for automatic differentiation derived CFD codes. Computers & Fluids 46:1, pages 174-179.
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Patick Heimbach, Dimitris Menemenlis, Martin Losch, Jean-Michel Campin & Chris Hill. (2010) On the formulation of sea-ice models. Part 2: Lessons from multi-year adjoint sea-ice export sensitivities through the Canadian Arctic Archipelago. Ocean Modelling 33:1-2, pages 145-158.
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Ralf Giering, Thomas Kaminski, Bernhard Eisfeld, Nicolas Gauger, Jochen Raddatz & Lars Reimer. 2009. MEGADESIGN and MegaOpt - German Initiatives for Aerodynamic Simulation and Optimization in Aircraft Design. MEGADESIGN and MegaOpt - German Initiatives for Aerodynamic Simulation and Optimization in Aircraft Design 221 235 .
Bradley M. Bell & James V. Burke. 2008. Advances in Automatic Differentiation. Advances in Automatic Differentiation 67 77 .
V. Rath, A. Wolf & H. M. Bücker. (2006) Joint three-dimensional inversion of coupled groundwater flow and heat transfer based on automatic differentiation: sensitivity calculation, verification, and synthetic examples. Geophysical Journal International 167:1, pages 453-466.
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R. Giering, T. Kaminski & T. Slawig. (2005) Generating efficient derivative code with TAF. Future Generation Computer Systems 21:8, pages 1345-1355.
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Ralf Giering & Thomas Kaminski. (2003) Applying TAF to generate efficient derivative code of Fortran 77‐95 programs. PAMM 2:1, pages 54-57.
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Michael Bartholomew-Biggs, Steven Brown, Bruce Christianson & Laurence Dixon. (2000) Automatic differentiation of algorithms. Journal of Computational and Applied Mathematics 124:1-2, pages 171-190.
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Dmitri Goloubentsev, Evgeny Lakshtanov & Vladimir Piterbarg. (2021) Automatic Implicit Function Theorem. SSRN Electronic Journal.
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Luca Capriotti, Yupeng Jiang & Andrea Macrina. (2015) Real-Time Risk Management: An AAD-PDE Approach. SSRN Electronic Journal.
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Marc P. A. Henrard. (2013) Algorithmic Differentiation in Finance: Root Finding and Least Square Calibration. SSRN Electronic Journal.
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Marc P. A. Henrard. (2011) Adjoint Algorithmic Differentiation: Calibration and Implicit Function Theorem. SSRN Electronic Journal.
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