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Title

On the convergence rate of regularization methods for ill-posed extremal problems

Authors 1, 2

Affiliations

  1. Department of Computer Science, Loránd Eötvös University, Budapest 112, P.O. Box 157, H-1502 Hungary
  2. Faculty of Computational Mathematics and Cybernetics, Moscow State University, GSP, Leninskie Gory, 119899 Moscow, Russia

Bibliography

  1. V. A. Bereznev, V. G. Karmanov and A. A. Tret'yakov, Stable methods of solving extremal problems with approximate information, preprint, Scientific Council for the Complex Problem 'Cybernetics', Acad. Sci. USSR, 1987 (in Russian).
  2. M. Kovács, On the regularization of not well-posed extremal problems using a barrier function, in: Numerical Analysis, Computer Centers, Moscow Univ. and Budapest Univ., 1978, 62-78 (in Russian).
  3. M. Kovács, On the convergence of the method of generalized barrier functions, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. 1981 (1), 40-45 (in Russian).
  4. M. Kovács and F. P. Vasil'ev, On the convergence rate of the continuous version of the regularized gradient method, Optimization 18 (5) (1987), 689-696.
  5. M. Kovács and F. P. Vasil'ev, Convergence rate for regularized barrier function methods, ibid. 22 (3) (1991), 427-438.
  6. V. V. Morozov and M. Yachimovich, An estimate of convergence rate of a regularization method for a linear programming problem, in: Computational Complexes and Modelling of Complex Systems, Izdat. Moskov. Gos. Univ., Moscow 1989, 134-138 (in Russian).
  7. A. N. Tikhonov and V. Ya. Arsenin, Methods for the Solution of Ill-Posed Problems, Nauka, Moscow 1986 (in Russian).
  8. A. N. Tikhonov and F. P. Vasil'ev, Methods of solution of ill-posed extremal problems, in: Mathematical Models and Numerical Methods, Banach Center Publ. 3, PWN, Warszawa 1978, 297-342 (in Russian).
  9. A. N. Tikhonov, F. P. Vasil'ev, M. M. Potapov and A. D. Yuriĭ, Regularization of minimization problems on sets given approximately, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. 1977 (1), 4-19 (in Russian).
  10. F. P. Vasil'ev, Methods of Solution of Extremal Problems, Nauka, Moscow 1981 (in Russian).
  11. F. P. Vasil'ev, On the regularization of ill-posed extremal problems, Dokl. Akad. Nauk SSSR 241 (5) (1978), 1001-1004 (in Russian).
  12. F. P. Vasil'ev, Regularization of ill-posed minimization in approximately specified sets, Zh. Vychisl. Mat. i Mat. Fiz. 20 (1) (1980) (in Russian).
  13. F. P. Vasil'ev, Regularization of unstable minimization problems, Trudy Mat. Inst. Steklov. 185 (1988), 60-65 (in Russian).
  14. F. P. Vasil'ev, A residual method for solving unstable minimization problems, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. 1987 (4), 6-10, 72 (in Russian).
  15. F. P. Vasil'ev, Regularization methods for unstable minimization problems, based on the set extension, ibid. 1990 (1), 3-16 (in Russian).
  16. F. P. Vasil'ev, An estimate of the rate of convergence of A. N. Tikhonov's regularization method for nonstable minimization problems, Dokl. Akad. Nauk SSSR 299 (4) (1988), 792-796 (in Russian).
  17. F. P. Vasil'ev, An estimate of the convergence rate of regularization methods for unstable minimization problems, in: Direct and Inverse Problems of Mathematical Physics, Izdat. Moskov. Gos. Univ., Moscow 1991, 115-122 (in Russian).
  18. F. P. Vasil'ev, Numerical Methods for Solving Extremal Problems, Nauka, Moscow 1988 (in Russian).
  19. F. P. Vasil'ev, An estimate for the convergence rate of the quasisolution method for a linear programming problem, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. 1991 (1), 16-22 (in Russian).
  20. F. P. Vasil'ev, A. Yu. Ivanitskiĭ and V. A. Morozov, An estimate for the rate of convergence of the residual method for problems of linear programming with approximate data, Zh. Vychisl. Mat. i Mat. Fiz. 30 (8) (1990), 1257-1262, 1279 (in Russian).
  21. F. P. Vasil'ev and M. Kovács, Regularization of ill-posed extremal problems with imprecisely given initial data, in: Computationl Mathematics, Banach Center Publ. 13, PWN, Warszawa 1984, 297-341 (in Russian).
  22. F. P. Vasil'ev and M. Kovács, Regularization of ill-posed extremal problems in connection with penalty functions of general type, in: Problems of Computational Mathematics and System Analysis, Computer Centers, Moscow Univ. and Budapest Univ., 1980, 19-41 (in Russian).
  23. F. P. Vasil'ev, M. Kovács, M. M. Potapov and Yu. N. Chekanov, An estimate of the convergence rate for a continuous analogue of the regularized gradient method for a linear programming problem, in: Numerical Methods for Solution of Boundary Value and Initial Value Problems for Differential Equations, Izdat. Moskov. Gos. Univ., Moscow 1986, 98-106 (in Russian).
  24. F. P. Vasil'ev and M. A. Kurzhanskiĭ, On the method of quasisolution for unstable problems of minimization with imprecisely defined initial data, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. 1989 (4), 13-18 (in Russian).
  25. F. P. Vasil'ev, V. V. Morozov and M. Yachimovich, An estimate for the rate of convergence of a regularization method for a linear programming problem, Zh. Vychisl. Mat. i Mat. Fiz. 29 (4) (1989), 631-635 (in Russian).
  26. F. P. Vasil'ev, M. M. Potapov and Yu. N. Chekanov, An estimate for the rate of convergence of A. N. Tikhonov's regularization method for a linear programming problem, in: Mathematical Models and Numerical Methods, Izdat. Moskov. Gos. Univ., Moscow 1987, 21-27 (in Russian).
Banach Center Publications
1994/29/1
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Pages:
233-244
Main language of publication
English
Published
1994
Exact and natural sciences