Geodesic
Regularized dual method for nonlinear mathematical programming
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 5, pp. 796-816 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For a nonlinear programming problem with equality constraints in a Hilbert space, a dual-type algorithm is constructed that is stable with respect to input data errors. The algorithm is based on a modified dual of the original problem that is solved directly by applying Tikhonov regularization. The algorithm is designed to determine a norm-bounded minimizing sequence of feasible elements. An iterative regularization of the dual algorithm is considered. A stopping rule for the iteration process is given in the case of a finite fixed error in the input data. 
@article{ZVMMF_2007_47_5_a3,
     author = {M. I. Sumin},
     title = {Regularized dual method for nonlinear mathematical programming},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {796--816},
     year = {2007},
     volume = {47},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_5_a3/}
}
TY  - JOUR
AU  - M. I. Sumin
TI  - Regularized dual method for nonlinear mathematical programming
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2007
SP  - 796
EP  - 816
VL  - 47
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_5_a3/
LA  - ru
ID  - ZVMMF_2007_47_5_a3
ER  - 
%0 Journal Article
%A M. I. Sumin
%T Regularized dual method for nonlinear mathematical programming
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2007
%P 796-816
%V 47
%N 5
%U http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_5_a3/
%G ru
%F ZVMMF_2007_47_5_a3
M. I. Sumin. Regularized dual method for nonlinear mathematical programming. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 5, pp. 796-816. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_5_a3/

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

[2] Ishmukhametov A. Z., “Dvoistvennyi regulyarizovannyi metod resheniya odnogo klassa vypuklykh zadach minimizatsii”, Zh. vychisl. matem. i matem. fiz., 40:7 (2000), 1045–1060 | MR | Zbl

[3] Sumin M. I., “Optimalnoe upravlenie parabolicheskimi uravneniyami: dvoistvennye chislennye metody, regulyarizatsiya”, Raspredelennye sistemy: optimizatsiya i prilozheniya v ekonomike i naukakh ob okruzhayuschei srede, In-t matem. i mekhan. UrO RAN, Ekaterinburg, 2000, 66–69

[4] Sumin M. I., “Iterativnaya regulyarizatsiya gradientnogo dvoistvennogo metoda dlya resheniya integralnogo uravneniya Fredgolma pervogo roda”, Vestn. Nizhegorodskogo un-ta. Ser. Matem., 2004, no. 1(2), 192–208

[5] Sumin M. I., “Regulyarizovannyi gradientnyi dvoistvennyi metod resheniya obratnoi zadachi finalnogo nablyudeniya dlya parabolicheskogo uravneniya”, Zh. vychisl. matem. i matem. fiz., 44:11 (2004), 2001–2019 | MR | Zbl

[6] Sumin M. I., “Regulyarizovannyi dvoistvennyi algoritm v zadachakh optimalnogo upravleniya dlya raspredelennykh sistem”, Vestn. Nizhegorodskogo un-ta. Ser. Matem. modelirovanie i optimalnoe upravlenie, 2006, no. 2(31), 82–102

[7] Minu M., Matematicheskoe programmirovanie. Teoriya i algoritmy, Nauka, M., 1990 | MR

[8] Uzawa H., “Iterative methods for concave programming”, Studies in Linear and Nonlinear Programming, Chap. 10, Univ. Press, Stanford, 1958 | Zbl

[9] Errou K. Dzh., Gurvits L., Udzava X., Issledovaniya po lineinomu i nelineinomu programmirovaniyu, Izd-vo inostr. lit., M., 1962

[10] Ekland I., Temam R., Vypuklyi analiz i variatsionnye problemy, Mir, M., 1979 | MR

[11] Glovinski R. Lions Zh.-L., Tremoler R., Chislennoe issledovanie variatsionnykh neravenstv, Mir, M., 1979 | MR

[12] Temam R., Uravneniya Nave–Stoksa. Teoriya i chislennyi analiz, Mir, M., 1981 | MR | Zbl

[13] Sumin M. I., “Regulyarizatsiya v zadachakh optimalnogo upravleniya i obratnykh zadachakh na osnove teorii dvoistvennosti”, Mezhdunar. konf. “Tikhonov i sovremennaya matematika”, Izd-vo VMiK MGU, M., 2006, 184–185

[14] Sumin M. I., “Regulyarizatsiya v lineino vypukloi zadache matematicheskogo programmirovaniya na osnove teorii dvoistvennosti”, Zh. vychisl. matem. i matem. fiz., 47:4 (2007), 602–625 | MR | Zbl

[15] Varga Dzh., Optimalnoe upravlenie differentsialnymi i funktsionalnymi uravneniyami, Nauka, M., 1977 | MR

[16] Levitin E. S., Teoriya vozmuschenii v matematicheskom programmirovanii i prilozheniya, Nauka, M., 1992 | MR | Zbl

[17] Bertsekas D., Uslovnaya optimizatsiya i metody mnozhitelei Lagranzha, Radio i svyaz, M., 1987 | MR | Zbl

[18] Golshtein E. G., Tretyakov N. V., Modifitsirovannye funktsii Lagranzha. Teoriya i metody optimizatsii, Nauka, M., 1989 | MR

[19] Oben Zh.-P., Ekland I., Prikladnoi nelineinyi analiz, Mir, M., 1988 | MR

[20] Bakushinskii A. B., Goncharskii A. B., Nekorrektnye zadachi. Chislennye metody i prilozheniya, Izd-vo MGU, M., 1989

[21] Bakushinskii A. B., Goncharskii A. B., Iterativnye metody resheniya nekorrektnykh zadach, Nauka, M., 1989 | MR