References
1. I. I. Dikin, “Investigation of optimal programming problems by the interior point method,” in: Optimization Methods [in Russian], Sci SO AN SSSR, Irkutsk (1975), pp. 72–108.
I. I. Dikin, “Finding a relatively interior point of a system of inequality and equality constraints,” in: Controlled Systems. Discrete Extremal Problems [in Russian], No. 17, Novosibirsk (1978), pp. 60-66.
I. I. Dikin, “Investigation of an inconsistent system of linear constraints by the interior point method,” in: Approximate Methods of Analysis and Their Applications [in Russian], Sci SO AN SSSR, Irkutsk (1987), pp. 52–59.
I. I. Dikin and O. M. Popova, Finding an Interior Feasible Point of a System of Linear Constraints [in Russian], Preprint No. 5, Sci SO RAN, Irkutsk (1995).
I. I. Dikin and O. M. Popova, Determination of Interior Feasible Points of Systems of Linear Constraints, Preprint No. 7, Sci SB RAS, Irkutsk (1995).
N. K. Karmarkar, “A new polynomial-time algorithm for linear programming,” Combinatorica, 4, No. 4, 373–395 (1984).
G. de Ghellinck and J.-Ph. Vial, “An extension of Karmarkar's algorithm for solving a system of linear homogeneous equations on the simplex,” Math. Program., 39, No. 1, 79–92 (1987).
T. Tsuchiya and K. Tanabe, “Local convergence properties of new methods in linear programming,” J. Oper. Res. Soc. Jpn., 33, No. 1, 22–45 (1990).
I. I. Dikin, “Determination of interior point of a system of linear inequalities,” Abstracts of Baikal School-Seminar on Methods of Optimization and Their Applications (1989), pp. 26-27.
T. Tsuchiya, Global Convergence of the Affine Scaling Methods for Degenerate Linear Programming Problems, Res. Memor. No. 373, Inst. Stat. Math., Tokyo, Japan (1990).
I. I. Dikin, “Determination of an interior point for a system of linear inequalities,” Kibern. Sist. Anal., No. 1, 67-74 (1992).
I. I. Dikin, Covergence of Dual Variables [in Russian], Preprint, Sci SO RAN, Irkutsk (1991).
P. Tseng and Z. Q. Luo, “On the convergence of the affine scaling algorithm,” Math. Program., 56, 301–319 (1992).
T. Tsuchiya and M. Muramatsu, Global Convergence of a Long-Step Affine Scaling Algorithm for Degenerate Linear Programming Problems, Res. Memor. No. 423, Inst. Stat. Math., Tokyo, Japan (1992).
O. Guler, D. den Hertog, C. Roos, et al., “Degeneracy in interior point methods for linear programing: a survey,” Ann. Oper. Res., 46, 107–138 (1993).
R. Saigal, Linear Programming: A Modern Integrated Analysis, Kluwer (1995).
I. I. Dikin and C. Roos, Convergence of the Dual Variables for the Primal Affine Scaling Method with Unit Steps in the Homogeneous Case, Rep. No. 94-69, Univ. of Technology, Delft, The Netherlands (1994).
I. I. Dikin, “Convergence of an iterative process,” in: Controlled Systems [in Russian], No. 12, Novosibirsk (1974), pp. 54–60.
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Translated from Kibernetika i Sistemnyi Analiz, No. 5, pp. 152–164, September–October, 1997.
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Dikin, I.I. Determination of an interior feasible point for a system of linear constraints. Cybern Syst Anal 33, 731–741 (1997). https://doi.org/10.1007/BF02667198
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DOI: https://doi.org/10.1007/BF02667198