Abstract
L.G. Khachiyan’s algorithm to check the solvability of a system of linear inequalities with integral coefficients is described. The running time of the algorithm is polynomial in the number of digits of the coefficients. It can be applied to solve linear programs in polynomial time.
This research was supported in part by National Science Foundation grant MCS-77-23738 and by Office of Naval Research contract N00014-76-C-0330. Reproduction in whole or in part is permitted for any purpose of the United States government.
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References
L.G. Khachiyan, “A polynomial algorithm for linear programming” (Russian), Doklady Akademii Nauk SSSR 244 (1979) 1093–1096.
N.Z. Shor “Convergence rate of the gradient descent method with dilatation of the space” (Russian), Kibernetika 2 (1970) 102–108.
A.S. Nemirovsky and D.B. Yudin, “Effective methods for solving convex programming problems of large size” (Russian), Ékonomika i Matematicčeskie Metody 15 (1979) 135–152.
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© 1981 The Mathematical Programming Society
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Gács, P., Lovász, L. (1981). Khachiyan’s algorithm for linear programming. In: König, H., Korte, B., Ritter, K. (eds) Mathematical Programming at Oberwolfach. Mathematical Programming Studies, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120921
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DOI: https://doi.org/10.1007/BFb0120921
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