Abstract

In the article, a comparative analysis of the packets of fast automatic differentiation Adept, CoDiPack and FADBAD is carried out. The example of the inverse coefficient problem shows the advantage of the direct method of fast automatic differentiation implemented in the CoDiPack package over the direct and inverse methods implemented in the Adept package and over the direct method implemented in the FADBAD package. As numerical optimization methods, the gradient descent method and the Levenberg-Marquardt method were used. Recommendations are given on the choice of optimization methods and rapid automatic differentiation, depending on the dimension of the problem.

Keywords:

optimal control, fast automatic differentiation, gradient, Jacobi matrix, Levenberg-Marquardt method.

pp. 30-36 

References

1. Ajda-Zade K.R., Evtushenko Ju.G. Bystroe avtomaticheskoe differencirovanie // Matematicheskoe modelirovanie, 1989. T. 1, S. 121-139.
2. Evtushenko Y.G., Mazurik V.P. Matematicheskoe obespechenie optimizacii. M: Znanie. 1989.
3. Evtushenko Y.G. Automatic differentiation viewed from optimal control theory // Proceedings of the Workshop on Automatic
4. Differentiation of Algorithms: Theory, Implementation and Application. Philadelphia: SIAM, 1991.
5. Griewank A, Corliss G.F., eds. Automatic Differentiation of Algoritms. Theory, Implementation and Application. Philadelphia: SIAM, 1991.
6. Evtushenko J.G., Zubov V.I. Ob obobshhjonnoj metodologii bystrogo avtomaticheskogo differencirovanija // Zh. vychisl. matem. i matem. fiz. 2016. T. 56. № 11, S. 1847–1862.
7. Albu A. F., Zubov V. I. Ob jeffektivnosti reshenija zadach optimal'nogo upravlenija s pomoshh'ju metodologii bystrogo avtomaticheskogo differencirovanija //Trudy Instituta matematiki i mehaniki UrO RAN. – 2015. – T. 21. – №. 4. – S. 20-29.
8. Hogan R. J. Fast reverse-mode automatic differentiation using expression templates in C++ //ACM Transactions on Mathematical Software (TOMS). – 2014. – T. 40. – №. 4. – S. 26.
9. Albring T. et al. An aerodynamic design framework based on algorithmic differentiation //ERCOFTAC Bull. – 2015. – T. 102. – S. 10-16.
10. Bendtsen C., Stauning O. FADBAD, a flexible C++ package for automatic differentiation //Department of Mathematical Modelling, Technical University of Denmark. – 1996.
11. Zubov V. I., “Primenenie metodologii bystrogo avtomaticheskogo differencirovanija k resheniju obratnoj kojefficientnoj zadachi dlja uravnenija teploprovodnosti”, Zh. vychisl. matem. i matem. fiz., 56:10 (2016), 1760–1774; Comput. Math. Math. Phys., 56:10 (2016), 1743–1757
12. Evtushenko Y. G. Optimizacija i bystroe avtomaticheskoe differencirovanie //M.: Nauchnoe izdanie VC RAN. – 2013.
13. A. Griewank and A. Walther. 2008. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation 2nd Ed. SIAM.
14. Gill F., Murray U., Rait M. Prakticheskaja optimizacija. – 1985.