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

Banach Center Publications (1994)

- Volume: 29, Issue: 1, page 233-244
- ISSN: 0137-6934

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topKovács, M., and Vasil'ev, F.. "On the convergence rate of regularization methods for ill-posed extremal problems." Banach Center Publications 29.1 (1994): 233-244. <http://eudml.org/doc/262859>.

@article{Kovács1994,

author = {Kovács, M., Vasil'ev, F.},

journal = {Banach Center Publications},

keywords = {ill-posed extremal problems; penalty function method; nonlinear programming problem; regularization methods; method of stabilization; method of residuals; method of quasisolutions; barrier function methods},

language = {eng},

number = {1},

pages = {233-244},

title = {On the convergence rate of regularization methods for ill-posed extremal problems},

url = {http://eudml.org/doc/262859},

volume = {29},

year = {1994},

}

TY - JOUR

AU - Kovács, M.

AU - Vasil'ev, F.

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

JO - Banach Center Publications

PY - 1994

VL - 29

IS - 1

SP - 233

EP - 244

LA - eng

KW - ill-posed extremal problems; penalty function method; nonlinear programming problem; regularization methods; method of stabilization; method of residuals; method of quasisolutions; barrier function methods

UR - http://eudml.org/doc/262859

ER -

## References

top- [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. Zbl0647.90070
- [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).

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