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Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics.
[author] Karush, WW. (1939). Minima of Functions of Several Variables with Inequalities as Side Constraints. (M.Sc. thesis). Dept. of Mathematics, Univ. of Chicago, Chicago, Illinois
1939
Earlier work this paper cites.
[author] Kuhn, H. W.H. W. and Tucker, A. W.A. W. (1951). Nonlinear programming. Proceedings of 2nd Berkeley Symposium 481–492
1951
Earlier work this paper cites.
[author] Pontryagin, LSL., Boltyanskii, VGV., Gamkrelidze, RVR. and Mishechenko, EFE. (1963). The Mathematical Theory of Optimal Processes
1963
Earlier work this paper cites.
[author] Errico, MM. (1997). What is an adjoint model? Bulletin of the American Meteorological Society 78 2577 – 2591
1997
Earlier work this paper cites.
2002
Earlier work this paper cites.
[author] Cao, YY., Li, ShengtaiS., Petzold, LL. and R, SerbanS. (2002). Adjoint Sensitivity Analysis for Differential-Algebraic Equations: The Adjoint DAE System and Its Numerical Solution. SIAM Journal on Scientific Computing 24 1076 – 1089
2002
Earlier work this paper cites.
[author] Bell, Bradley MB. M. and Burke, James VJ. V. (2008). Algorithmic Differentiation of Implicit Functions and Optimal Values. In Advances in Automatic Differentiation. Lecture Notes in Computational Science and Engineering, (C. HC. H. Bischof, H. MH. M. Bücker, PP. Hovland, UU. Naumann and JJ. Utke, eds.) 64 Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68942-3_17
2008
Earlier work this paper cites.
[author] Griewank, AndreasA. and Walther, AndreaA. (2008). Evaluating derivatives, Second ed. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
2008
Cited alongside, same era.
[author] Carpenter, BobB., Hoffman, Matthew D.M. D., Brubaker, Marcus A.M. A., Lee, DanielD., Li, PeterP. and Betancourt, Michael J.M. J. (2015). The Stan Math Library: Reverse-Mode Automatic Differentiation in C++. arXiv 1509.07164
2015
Cited alongside, same era.
[author] Carpenter, BobB., Gelman, AndrewA., Hoffman, MattM., Lee, DanielD., Goodrich, BenB., Betancourt, MichaelM., Brubaker, Marcus A.M. A., Guo, JiqiangJ., Li, PeterP. and Riddel, AllenA. (2017). Stan: A Probabilistic Programming Language. Journal of Statistical Software 76 1 –32. 10.18637/jss.v076.i01
2017
Cited alongside, same era.
2018
Later among the works it cites.
[author] Lorraine, JJ., Vicol, PP. and Duvenaud, DD. (2019). Optimizing Millions of Hyperparameters by Implicit Differentiation. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108 1540 – 1552
2019
Later among the works it cites.
[author] Margossian, Charles C.C. C. (2019). A Review of automatic differentiation and its efficient implementation. Wiley interdisciplinary reviews: data mining and knowledge discovery 9. 10.1002/WIDM.1305
2019
Later among the works it cites.
[author] Hindmarsh, AA. and Serban, RR. (2020). User Documentation for CVODES v5.1.0. Technical Report
2020
Later among the works it cites.
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2017
Cited alongside, same era.
[author] Baydin, Atilim GunesA. G., Pearlmutter, Barak A.B. A., Radul, Alexey AndreyevichA. A. and Siskind, Jeffrey MarkJ. M. (2018). Automatic differentiation in machine learning: a survey. Journal of Machine Learning Research 18 1 – 43
2018
Cited alongside, same era.
2018
Cited alongside, same era.
[author] Bradbury, JamesJ., Frostig, RoyR., Hawkins, PeterP., Johnson, Matthew JamesM. J., Leary, ChrisC., Maclaurin, DougalD., Necula, GeorgeG., Paszke, AdamA., VanderPlas, JakeJ., Wanderman-Milne, SkyeS. and Zhang, QiaoQ. (2018). JAX: composable transformations of Python+NumPy programs
2018
Cited alongside, same era.
[author] Kesavan, S.S. (2020). Nonlinear functional analysis—a first course, second ed. Texts and Readings in Mathematics 28. Hindustan Book Agency, New Delhi. 4288179
2020
Later among the works it cites.
[author] Li, XuechenX., Wong, Leonard Ting-KamL. T.-K., Chen, Ricky T. Q.R. T. Q. and Duvenaud, DavidD. (2020). Scalable Gradients for Stochastic Differential Equations. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR
2020
Later among the works it cites.
[author] Gaebler, Johann DJ. D. (2021). Autodiff for Implicit Functions in Stan
2021
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