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An iterative method, having linear rate of convergence, for solving a pair of dual linear programs. (English) Zbl 0259.90019


MSC:

90C05 Linear programming
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[1] S. Agmon, ”The relaxation method for linear inequalities,”Canadian Journal of Mathematics 6 (1954) 382–392. · Zbl 0055.35001 · doi:10.4153/CJM-1954-037-2
[2] R.W. Cottle, ”Symmetric dual quadratic programs,”Quarterly of Applied Mathematics 21 (1963) 237–243. · Zbl 0127.36802
[3] C.W. Cryer, ”The solution of a quadratic programming problem using systematic overrelaxation,”SIAM Journal on Control 9 (1971) 385–392. · Zbl 0216.54603 · doi:10.1137/0309028
[4] I.I. Eremin and V.D. Mazurov, ”Iterative method for solving convex programming problems,”Soviet Physics Doklady 11 (1967) 757–759. · Zbl 0155.28404
[5] V.M. Fridman and V.S. Chernina, ”An iteration process for the solution of the finitedimensional contact problem,”USSR Computational Mathematics and Mathematical Physics 7 (1) (1967) 210–214. · Zbl 0191.15901 · doi:10.1016/0041-5553(67)90071-7
[6] N. Gastinel, ”Sur certains procédés itératifs non linéaires de résolution de systèmes d’équations du premier degré,” in:Information Processing 1962, Ed. C.M. Popplewell (North-Holland, Amsterdam, 1963) 97–100.
[7] H.P. Künzi, W. Krelle and W. Oettli,Nonlinear programming (Blaisdell Publishing Co., Waltham, Mass., 1966).
[8] W. Oettli, ”Méthodes itératives, de convergence linéaire, pour résoudre des problèmes de programmation et d’approximation linéaires,”Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences de Paris, Série A, 272 (1971) 680–682. · Zbl 0214.42304
[9] B.T. Polyak, ”Gradient methods for solving equations and inequalities,”USSR Computational Mathematics and Mathematical Physics 4 (6) (1964) 17–32. · Zbl 0147.35302 · doi:10.1016/0041-5553(64)90079-5
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