References
- Barbara A. Differential barrier property and strict quasi concavity in linear programming via concave gauges. Optimization. 2015;64(12). doi: https://doi.org/10.1080/02331934.2014.984705
- Wright SJ. Primal-dual interior-point methods. Philadelphia: SIAM; 1997.
- GAY DM. Electronic mail distribution of linear programming test problems. Math Program Soc Coal Newsletter. 1988;13:10–12.
- Tseng P, Bomze IM, Schachinger W. A first-order interior-point method for linearly constrained smooth optimization. Math Prog. 2011;127:399–424. doi: https://doi.org/10.1007/s10107-009-0292-7
- Barnes ER. A variation on Karmarkar's algorithm for solving linear programming problems. Math Prog. 1986;36:174–182. doi: https://doi.org/10.1007/BF02592024
- Vanderbei RJ, Meketon MS, Freedman BA. A modification of Karmarkar's linear programming algorithm. Algorithmica. 1986;1:395–407. doi: https://doi.org/10.1007/BF01840454
- Saigal R. A simple proof of a primal affine scaling method. Ann Oper Res. 1996;62:303–324. doi: https://doi.org/10.1007/BF02206821
- Monteiro RDC, Tsuchia T, Wang Y. A simplified global convergence proof of the affine scaling algorithm. Ann Oper Res. 1993;47:443–482. doi: https://doi.org/10.1007/BF02023109
- Tsen P, Luo ZQ. On the convergence of the affine-scaling algorithm. Math Prog. 1992;56:301–319. doi: https://doi.org/10.1007/BF01580904
- Tsuchiya T. Global convergence of the affine-scaling methods for degenerate linear programming problems. Math Prog. 1991;52:377–404. doi: https://doi.org/10.1007/BF01582896
- Dikin II. On the convergence of an iterative process. Upravlyaemye Sistemi. 1974;12:54–60. Russian.
- Todd MJ. A Dantzig-Wolfe-like variant of Karmarkar's interior point linear programming algorithm. Oper Res. 1990;38:1006–1018. doi: https://doi.org/10.1287/opre.38.6.1006
- Vanderbei RJ, Lagarias JC. Mathematical developments arising from linear programming. In: Lagarias JC and Todd MJ, editors. Proceedings of a joint summer research conference; Brunswick, ME, USA; 1988. Vol. 114 of Contemporary mathematics. Providence (RI): American Mathematical Society; 1990. p. 109–119.
- Vavassis SA. Stable numerical algorithms for equilibrium systems. Ithaca (NY): Cornell University; 1992.
- Barbara A, Crouzeix JP. Concave gauge functions and applications. Zeitschrift für Operation Research. 1994;40(1).
- Gondzio J, Makowski M. Hopdm – modular solver for LP problems, user's guide to version 2.12. Working paper WP-95-50. Laxenburg: International Institute for Applied Systems Analysis; 1995.
- Dolan ED, Moré JJ. Benchmarking optimization software with performance profiles. Math Program Ser A. 2002;91:201–213. doi: https://doi.org/10.1007/s101070100263
- Nesterov YE, Nemirowskii AS. Interior point polynomial methods in convex programming: theory and algorithms. Philadelphia: SIAM; 1994.
- Courant R. Varialtional methods for the solution of problems of equilibrium and vibrations. Bull Amer Math Soc. 1943;49:1–23. doi: https://doi.org/10.1090/S0002-9904-1943-07818-4
- Frisch KR. The logarithmic potential method of convex programming. Oslo: University Institute of Economics; 1955.
- Auslender A. Optimisation, méthodes numériques. MASSON; 1976.
- Dikin II. Iterative solution of problems of linear and quadratic programming. Sov Math Doklady. 1967;8:674–675.
- Karmakar N. A new polynomial time algorithm for linear programming. Combinatorica. 1984;4:373–395. doi: https://doi.org/10.1007/BF02579150
- Roos C, Terlaky T, Vial J-Ph. Interior point methods for mathematical programming. New York: Wiley; 1997.
- Monteiro RDC, Adler I, Resende MGC. A polynomial-time primal-dual affine scaling algorithm for linear and convex quadratic programming and its power series extension. Math Oper Res. 1990;15(2):191–214. doi: https://doi.org/10.1287/moor.15.2.191
- Jansen B, Roos C, Terlaky T. A polynomial primal-dual Dikin-type algorithm for linear programming. Math Oper Res. 1996;21(2):341–353. doi: https://doi.org/10.1287/moor.21.2.341
- Potra FA. Primal-dual affine scaling interior point methods for linear complementarity problems. SIAM J Optim. 2008;19(1):114–143. doi: https://doi.org/10.1137/060670341