Computation of exact gradients in distributed dynamic systems

Optimization Methods and Software

Volumn 9, Issue 1-3, 1998, Pages 45-75

  Evtushenko, Yuri ^a  

^a RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

Author keywords

Adjoint equation; Differentiation of elementary functions; Fast automatic differentiation; Hyperbolic system; Optimal control problem; Parabolic system; Rounding error estimation; Sensitivity analysis

Indexed keywords

DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); DISTRIBUTED PARAMETER CONTROL SYSTEMS; FUNCTION EVALUATION; OPTIMAL CONTROL SYSTEMS; SENSITIVITY ANALYSIS;

DISCRETIZATION SCHEME; FIRST ORDER DERIVATIVES;

NONLINEAR PROGRAMMING;

EID: 0031706694     PISSN: 10556788     EISSN: None     Source Type: Journal    
DOI: 10.1080/10556789808805686     Document Type: Article

References (23)

1. Aida-Zade, K. R. and Evtushenko, Y. G. (1989). Fast automatic differentiation, Mathematical Modeling, 1, 121-139, [in Russian].
2. Baur, W. and Strassen, V. (1983). The complexity of partial derivatives, Theoretical Computer Sciences, 22, 317-320.
3. Bertsekas, D. (1982). Constrained optimization and Lagrange multiplier methods, Academic Press, New York.
4. Caratheodory, C. (1956). it Variationsrechnung und partielle Differentialgleichungen erster Ordnung, Band 1, Leipzig.
5. Evtushenko, Y. G. and Mazouric, V. P. (1989). Optimization Sofware, Znanie, Moscow, [in Russian].
6. Evtushenko, Y. G. (1991). Automatic differentiation viewed from optimal control theory, in [9], 25-30.
7. Evtushenko, Y. G. (1985). Numerical Optimization Techniques, Optimization Software, Inc., Publications Division, New York.
8. Grachev, N. I. and Evtushenko, Y. G. (1980). A library of programs for solving optimal control problems, U.S.S.R. Comput. Maths. Math. Phys., (Pergamon Press), 19, 99-119.
9. Griewank, A. (1989). On automatic differentiation, in M. Iri and K. Tanabe (Eds.) Mathematical Programming: Recent Developments and Applications, Kluwer Academic Publishers, 83-108.
10. Griewank, A. and Corliss, G. F. Eds. (1991). Automatic Differentiation of Algorithms. Theory, Implementation and Application, SIAM, Philadelphia.
11. Griewank, A. (1992). Achieving logarithmic growth of temporal and spatial complexity in reverse automatic differentiation, Optimization Methods and Sofware, 1, 35-54.
12. Iri, M. (1991). History of Automatic differentiation and rounding error estimation. In [9], 3-16.
13. Iri, M. (1984). Simultaneous computation of functions, partial derivatives and estimates of rounding errors - Complexity and practicality, Japan Journal of Applied Mathematics, 1, 223-252.
14. Iri, M. and Kubota, K. (1987). Methods of fast automatic differentiation and applications, Research memorandum RMI 87-02. Department of Mathematical Engineering and Instrumental Physics, Faculty of Engineering, University of Tokyo.
15. Kim, K., Nesterov, Y., Skokov, V. and Cherkaslkij, B. (1984). Efficient algorithm for differentiation and extremal problem, Economy and Mathematical Methods, 20, 309-318, [in Russian].
16. Lellouche, J. M., Devenon, J. L. and Dekeyser, I.(1994). Boundary control of Burger's equation - A numerical approach, Computers and Mathematics with Applications, 28(5), 33-44.
17. Marchuk, G. I. (1992). Conjugate equations and analysis of complex systems, Science, Moscow, [in Russian].
18. Pontryagin, L. S., Boltyansky, V. G., Gamkrelidze, R. V. and Mitshenko, E. F. (1961). Mathematical Theory of Optimal Process, Nauka, Moscow.
19. Samarskii, A. A. (1971). Introduction to the Theory of Finite-difference Methods, Nauka, Moscow, [in Russian].
20. Stetter, H. J. (1973). Analysis of Discrimination Methods for Ordinary Differential Equations, Springer-Verlag, Berlin, Heidelberg, New York.
21. Teo, K. L and Wu, Z. S. (1984). Computation Methods for Optimizing Distributed Systems, Academic Press, Inc.
22. Teo, K. L., Goh, C. J. and Wong, K. H. (1991). A Unified Computation Approach to Optimal Control Problems, Longman Scientific and Technical, England.
23. Vasiliev F. P. (1981). Numerical Methods for Solving Optimization Problems, Nauka, Moscow, [in Russian].