Geodesic
Tikhonov Regularization for General Nonlinear Constrained Optimization Problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 10, pp. 1651-1656 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The goal of this study is to analyze the Tikhonov regularization method as applied to a general nonlinear optimization problem that has been previously reduced to an unconstrained optimization problem. The stability properties of the method are examined, and its convergence is proved. 
@article{ZVMMF_2007_47_10_a0,
     author = {B. Nguyen},
     title = {Tikhonov {Regularization} for {General} {Nonlinear} {Constrained} {Optimization} {Problem}},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1651--1656},
     year = {2007},
     volume = {47},
     number = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_10_a0/}
}
TY  - JOUR
AU  - B. Nguyen
TI  - Tikhonov Regularization for General Nonlinear Constrained Optimization Problem
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2007
SP  - 1651
EP  - 1656
VL  - 47
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_10_a0/
LA  - en
ID  - ZVMMF_2007_47_10_a0
ER  - 
%0 Journal Article
%A B. Nguyen
%T Tikhonov Regularization for General Nonlinear Constrained Optimization Problem
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2007
%P 1651-1656
%V 47
%N 10
%U http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_10_a0/
%G en
%F ZVMMF_2007_47_10_a0
B. Nguyen. Tikhonov Regularization for General Nonlinear Constrained Optimization Problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 10, pp. 1651-1656. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_10_a0/

[1] Fletcher R., Reeves C., “Function minimization by conjugate gradients”, Comput. J., 7 (1964), 149–154 | DOI | MR | Zbl

[2] Polak E., Ribiére G., “Note sur la convergence de directions conjugees”, Rev. Francaise Inform. Rech. Operat., 16 (1969), 35–43 | MR | Zbl

[3] Polyak B. T., “Metod sopryazhennykh gradientov v zadachakh na ekstremum”, Zh. vychisl. matem. i matem. fiz., 9:4 (1969), 807–821 | Zbl

[4] Hestenes M. R., Stiefel E. L., “Methods of conjugate gradients for solving linear systems”, Res. Nat. Bur. Standards Sect., 5 (1952), 409–436 | MR

[5] Yuan Y., “On the trancated conjugate gradient method”, Math. Program., 87 (2000), 561–571 | DOI | MR

[6] Yuan Y., “A class of globally convergent conjugate gradient methods”, Science in China, 46 (2003), 253–261 | MR

[7] Yuan Y., “A new stepsize for the steepest descent method”, J. Comput. Math., 24 (2006), 149–156 | MR | Zbl

[8] Powell M. J. D., “A new algorithm for unconstrained optimization”, Nonlinear Program., Acad. Press, New York, 1970, 31–66 | MR

[9] Powell M. J. D., “Convergence properties of a class of minimization problems”, Nonlinear Program., v. 2, Acad. Press, New York, 1975, 1–27 | MR

[10] Powell M. J. D., “On the global convergence of trust region algorithm for unconstrained optimization”, Math. Program., 29 (1984), 297–303 | DOI | MR | Zbl

[11] Powell M. J. D., Yuan Y., “A trust region algorithm for equality constrained optimization”, Math. Program., 49 (1991), 189–211 | DOI | MR

[12] Vardi A., “A trust region algorithm for equality constrained minimization: convergence properties and implementation”, SIAM J. Numer. Analys., 4 (1985), 575–591 | DOI | MR

[13] Yuan Y., “On the convergence of a new trust region algorithm”, Numer. Math., 70 (1995), 515–539 | DOI | MR | Zbl

[14] Vasilev F. P., Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1988 | MR

[15] Vasilev F. P., Metody optimizatsii, Faktorial Press, M., 2002

[16] Nguyen Bitong, “Regularization for unconstrained vector optimization of convex functionals in Banach spaces”, Zh. vychisl. matem. i matem. fiz., 46:3 (2006), 372–378 | MR | Zbl

[17] Nguyen Buong, “Convergence rates and finite-dimensional approximations for a class of ill-posed variational inequalities”, Ukrainskii matem. zhurnal, 48 (1996), 1–9 | MR

[18] Nguyen Buong, Phan Vam Loi, “On parameter choice and convergence rates in regularization for a class of ill-posed variational inequalities”, Zh. vychisl. matem. i matem. fiz., 44:10 (2004), 1735–1744 | MR | Zbl

[19] Kluge R., “Optimal control with minimum problems and variational inequalities”, Lect. Notes Comput. Sci., 27, 1975, 375–382

[20] Ryazantseva I. P., “Operatornyi metod regulyarizatsii dlya optimalnogo resheniya zadach s monotonnymi otobrazheniyami”, Sibirskii matem. zhurnal, 24 (1983), 455–456

[21] Tikhonov A. N., Arsenin V. Ya., Metody resheniya plokho obuslovlennykh zadach, Nauka, M., 1979 | MR