@article{ZVMMF_1999_39_1_a2,
author = {V. G. Zhadan},
title = {Primal-dual {Newton} method for linear programming problems},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {17--32},
year = {1999},
volume = {39},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1999_39_1_a2/}
}
V. G. Zhadan. Primal-dual Newton method for linear programming problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 39 (1999) no. 1, pp. 17-32. http://geodesic.mathdoc.fr/item/ZVMMF_1999_39_1_a2/
[1] Kojima M., Mizuno S., Yoshise A., “A primal-dual interior point method for linear programming”, Progress Math. Program. Interior Point and Related Methods, Springer, Berlin, 1989, 29–47 | MR
[2] Monteiro R. C., Adler I., “Interior path-following primal-dual algorithms. Part I: linear programming”, Math. Program., 44 (1989), 27–41 | DOI | MR | Zbl
[3] Todd M. J., Ye Y., “A centered projective algorithm for linear programming”, Math. Operat. Res., 15 (1990), 508–529 | DOI | MR | Zbl
[4] Mizuno S., Todd M. J., Ye Y., On adaptive step primal-dual interior-point algorithms for linear programming, Techn. Rept. 944. Scool Operat. Res. and Industr. Engng., Cornell Univ., New York, Ithaca, 1990, 14853–3801
[5] Gonzaga C., “Path following methods for linear programming”, SIAM Rev., 34:2 (1992), 167–224 | DOI | MR | Zbl
[6] Choi I. C., Monma I. C., Shanno D. F., “Father development of a primal-dual interior point method for linear programming”, ORSA J. Comput., 2 (1990), 304–311 | Zbl
[7] Jansen B., Roos C., Terlaky T., Vial J.-Ph., Primal-dual target-following algorithms for linear programming, Rept. No 93-107, Delft Univ. Technol., 1993
[8] Lustig I. J., Marsten R. E., Shanno D. F., “Computational experience with a primal-dual interior point method for linear programming”, Linear Algebra and Appl., 152 (1989), 191–222 | DOI | MR
[9] Lustig I. J., Marsten R. E., Shanno D. F., “On implementing Mehrotra's predictor-corrector interior point method for linear programming”, SIAM J. Optimizat., 2 (1992), 435–449 | DOI | MR | Zbl
[10] Mehrotra S., “Quadratic convergence in primal-dual methods”, Math. Operat. Res., 18 (1993), 741–751 | DOI | MR | Zbl
[11] Roos C., Terlaky T., Vial J.-Ph., Theory and algorithms for linear optimization. An interior point approach, John Wiley Sons, New York etc., 1997 | MR
[12] Wright S. J., Primal-dual interior-point methods, SIAM, Philadelphia, 1997 | MR
[13] Zhang Y., Tapia R. A., “Superlinear and quadratic convergence of primal-dual interior point methods for linear programming”, SIAM J. Optimizat., 3 (1993), 118–133 | DOI | Zbl
[14] Evtushenko Yu., Zhadan V., “Stable barrier-projection and barrier-Newton methods in nonlinear programming”, Optimizat. Meth. and Software, 3 (1994), 237–356 | DOI | MR
[15] Evtushenko Yu. G., Zhadan V. G., Cherenkov A. P., “Primenenie metoda Nyutona k resheniyu zadach lineinogo programmirovaniya”, Zh. vychisl. matem. i matem. fiz., 35:6 (1995), 850–866 | MR | Zbl
[16] Stanevichyus A.-I. A., Scherbak L. V., “Novye varianty barerno-nyutonovskikh metodov dlya resheniya zadach lineinogo programmirovaniya”, Zh. vychisl. matem. i matem. fiz., 35:12 (1995), 1796–1807 | MR | Zbl
[17] El-Bakry A. S., Tapia R. A., Zhang Y., “A study of indicators for identifying zero variables in interior-point methods”, SIAM Rev., 36:1 (1994), 45–72 | DOI | MR | Zbl
[18] Zhadan V. G., “Metod Nyutona s naiskoreishim spuskom dlya zadach lineinogo programmirovaniya”, Soobsch. po vychisl. matem., VTs RAN, M., 1997 | MR