Geodesic
The use of Newton's method for linear programming
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 35 (1995) no. 6, pp. 850-866 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{ZVMMF_1995_35_6_a2,
     author = {Yu. G. Evtushenko and V. G. Zhadan and A. P. Cherenkov},
     title = {The use of {Newton's} method for linear programming},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {850--866},
     year = {1995},
     volume = {35},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1995_35_6_a2/}
}
TY  - JOUR
AU  - Yu. G. Evtushenko
AU  - V. G. Zhadan
AU  - A. P. Cherenkov
TI  - The use of Newton's method for linear programming
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1995
SP  - 850
EP  - 866
VL  - 35
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1995_35_6_a2/
LA  - ru
ID  - ZVMMF_1995_35_6_a2
ER  - 
%0 Journal Article
%A Yu. G. Evtushenko
%A V. G. Zhadan
%A A. P. Cherenkov
%T The use of Newton's method for linear programming
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1995
%P 850-866
%V 35
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_1995_35_6_a2/
%G ru
%F ZVMMF_1995_35_6_a2
Yu. G. Evtushenko; V. G. Zhadan; A. P. Cherenkov. The use of Newton's method for linear programming. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 35 (1995) no. 6, pp. 850-866. http://geodesic.mathdoc.fr/item/ZVMMF_1995_35_6_a2/

[1] Ortega D., Reinboldt V., Iteratsionnye metody resheniya nelineinykh uravnenii so mnogimi neizvestnymi, Mir, M., 1975

[2] Vasilev F. P., Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1980 | MR

[3] Evtushenko Yu. G., Metody resheniya ekstremalnykh zadach i ikh primenenie v sistemakh optimizatsii, Nauka, M., 1982 | MR | Zbl

[4] Iri M., Imai H., “A multiplicative barrier function method for linear programming”, Algorithmica, 1 (1986), 455–482 | DOI | MR | Zbl

[5] De Ghellink G., Vial J.-P., “A polynomial Newton method for linear programming”, Algorithmica, 1 (1986), 425–453 | DOI | MR

[6] Renegar J., “A polynomial-time algorithm, based on Newton's method for linear programming”, Math. Program., 40:1 (1988), 55–94 | MR

[7] Gonzaga C. C., “Path-following methods for linear programming”, SIAM Rev., 34:2 (1992), 167–224 | DOI | MR | Zbl

[8] Kojima M., Mizuno S., Yoshise A., “A primal-dual interior point method for linear programming”, Progress Math. Program. Interior Point and Relative Methods, Ch. 2, eds. N. Megiddo, Springer-Verlag, Berlin, 1989 | MR

[9] Monteiro R. C., Adler I., “Interior path-following primal-dual algorithm, part I: Linear programming”, Math. Program., 44 (1989), 43–66 | DOI | MR | Zbl

[10] McShane K., Monma C., Shanno D., “An implementation of a primal-dual interior point method for linear programming”, ORSA J. Comput., 1 (1989), 70–83 | Zbl

[11] Ye Y., Tapia R., Zhang Y., A superlinear convergent $O(\sqrt n L)$-iteration algorithm for linear programming, Techn. Rept TR91-22, Rice Univ., Houston, Texas, 1991

[12] Jansen B., Roos C., T. Terlaky, Vial J.-Ph., Primal-dual target-following algorithms for linear programming, Techn. Rept 93-107, Fac. Techn. Math. and Informatics, TU Delft, 1993

[13] Eremin I. I., Astafev N. N., Vvedenie v teoriyu lineinogo i vypuklogo programmirovaniya, Nauka, M., 1976 | MR

[14] Evtushenko Yu. G., Zhadan V. G., “The space transformation technique in mathematical programming”, System Modelling and Optimizat., Proc. 15th IFIP Conf., Lect. Notes in Control and Information Sci., 180, eds. P. Kall, Springer-Verlag, 1991 | MR

[15] Evtushenko Yu. G., Zhadan V. G., “Stable barrier-projection and barrier-Newton methods in nonlinear programming”, Optimizat Meth. and Software, 3 (1994), 237–256 | DOI | MR

[16] Evtushenko Yu. G., Zhadan V. G., “Barerno-proektivnye i barerno-nyutonovskie chislennye metody optimizatsii (sluchai nelineinogo programmirovaniya)”, Soobsch. po vychisl. matem., VTs AN SSSR, M., 1991

[17] Evtushenko Yu. G., Zhadan V. G., “Barerno-proektivnye i barerno-nyutonovskie chislennye metody optimizatsii (sluchai lineinogo programmirovaniya)”, Soobsch. po vychisl. matem., VTs RAN, M., 1992

[18] Ye Y., Line search in potential reduction algorithms for linear programming, Dept. Management Sci., Univ. Iowa, Iowa City, IA, 1989

[19] El-Bakly A. S., Tapia R. A., Zhang Y., A study of indicators for identifing zero variables in interior-point methods, Techn. Rept. TR91-15, Rice Univ., Houston, Texas, 1991