The gradient projection method for solving an optimal control problem

 Access to full text

 Full (PDF)

1. [1] A. G. Butkovskiĭ, Optimal Control Theory for Systems with Distributed Parameters, Nauka, Moscow, 1965 (in Russian). 
2. [2] Yn. V. Egorov, On some optimal control problems, Zh. Vychisl. Mat. i Mat. Fiz. 3 (1963), 887-904 (in Russian). Zbl0156.31804
3. [2] M. H. Farag, A numerical solution to a nonlinear problem of the identification of the characteristics of a mathematical model of heat exchange, in: Mathematical Modeling and Automated Systems, A. D. Iskenderov (ed.), Bakin. Gos. Univ., Baku, 1990, 23-30 (in Russian). Zbl0800.65015
4. [4] M. H. Farag and S. H. Farag, An existence and uniqueness theorem for one optimal control problem, Period. Math. Hungar. 30 (1995), 61-65. Zbl0821.49003
5. [5] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., 1964. Zbl0144.34903
6. [6] A. D. Iskenderov, On a certain inverse problem for quasilinear parabolic equations, Differentsial'nye Uravneniya 10 (1974), 890-898 (in Russian). Zbl0285.35040
7. [7] A. D. Iskenderov and R. K. Tagiev, Optimization problems with controls in coefficients of parabolic equations, ibid. 19 (1983), 1324-1334 (in Russian). Zbl0521.49016
8. [8] J.-L. Lions, Control problems in systems described by partial differential equations, in: Mathematical Theory of Control, A. V. Balakrishnan and L. W. Neustadt (eds.), Academic Press, New York and London, 1969, 251-271. 
9. [9] J.-L. Lions, Optimal Control by Systems Described by Partial Differential Equations, Mir, Moscow, 1972 (in Russian). 
10. [10] K. A. Lurie, Optimal Control in Problems of Mathematical Physics, Nauka, Moscow, 1975 (in Russian). 
11. [11] M. D. Madatov, Regularization of one class of optimal control problems, in: Approximate Methods and Computer, A. D. Iskenderov (ed.), Bakin. Gos. Univ., Baku, 1982, 78-80 (in Russian). 
12. [12] A. Mokrane, An existence result via penalty method for some nonlinear parabolic unilateral problems, Boll. Un. Mat. Ital. B 8 (1994), 405-417. Zbl0805.35068
13. [13] G. A. Phillipson and S. K. Mitter, Numerical solution of a distributed identification problem via a direct method, in: Computing Methods in Optimization Problems-2, L. A. Zadeh, L. W. Neustadt and A. V. Balakrishnan (eds.), Academic Press, New York, 1969, 305-315. Zbl0245.49020
14. [14] E. Polak, Computational Methods in Optimization, Academic Press, New York, 1971. 
15. [15] B. N. Pshenichnyĭ and Yu. M. Danilin, Numerical Methods in Extremal Problems, Mir, Moscow, 1982. 
16. [16] J. B. Rosen, The gradient projection method for nonlinear programming. Part I: Linear constraints, SIAM J. Appl. Math. 8 (1960), 181-217. Zbl0099.36405
17. [17] J. B. Rosen, The gradient projection method for nonlinear programming. Part II: Nonlinear constraints, ibid. 9 (1961), 514-532. Zbl0231.90048
18. [18] Ts. Tsachev, Optimal control of linear parabolic equation: The constrained right-hand side as control function, Numer. Funct. Anal. Optim. 13 (1992), 369-380. Zbl0767.49003
19. [19] F. P. Vasil'ev, Numerical Methods for Solving Extremal Problems, Nauka, Moscow, 1988 (in Russian).