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Cottle, Richard W.; Dantzig, George B.

Complementary pivot theory of mathematical programming. (English) Zbl 0155.28403

Linear Algebra Appl. 1, 103-125 (1968).
Reviewer: Kanti Swarup (New Delhi)
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Cited in 256 Documents

MSC:

90C05 Linear programming
90C20 Quadratic programming

Keywords:

linear programming; quadratic programming; bimatrix game; iteration
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\textit{R. W. Cottle} and \textit{G. B. Dantzig}, Linear Algebra Appl. 1, 103--125 (1968; Zbl 0155.28403)
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References:

[1] Cottle, R.W., Symmetric dual quadratic programs, Quart. appl. math., 21, 237-243, (1963) · Zbl 0127.36802
[2] Cottle, R.W., Nonlinear programs with positively bounded Jacobians, J. SIAM appl. math., 14, 147-158, (1966) · Zbl 0158.18903
[3] Dantzig, G.B., Linear programming and extensions, (1963), Princeton Univ. Press Princeton, New Jersey · Zbl 0108.33103
[4] Dantzig, G.B.; Cottle, R.W., Positive (semi-) definite programming, (), 55-73, Revised in · Zbl 0178.22801
[5] Dorn, W.S., Quality in quadratic programming, Quart. appl. math., 18, 155-162, (1960) · Zbl 0101.37003
[6] Du Val, P., The unloading problem for plane curves, Amer. J. math., 62, 307-311, (1940) · Zbl 0025.21102
[7] Farkas, J., Theorie der einfachen ungleichungen, J. reine angew. math., 124, 1-27, (1902) · JFM 32.0169.02
[8] Fiedler, M.; Ptak, V., On matrices with non-positive off-diagonal elements and positive principals minors, Czech. math. journal, 12, 382-400, (1962) · Zbl 0131.24806
[9] Fiedler, M.; Ptak, V., Some generalizations o positive definiteness and monotonicity, Numerische math., 9, 163-172, (1966) · Zbl 0148.25801
[10] Gale, D.; Nikaidŏ, H., The Jacobian matrix and global univalence of mappings, Math. ann., 159, 81-93, (1965) · Zbl 0158.04903
[11] Goldman, A.J., Resolution and separation theorems for polyhedral convex sets, () · Zbl 0072.37505
[12] Hall, M., Combinatorial theory, (1967), Blaisdell Waltham, Massachusetts, Chapter 16 · Zbl 0196.02401
[13] Kilmister, C.W.; Reeve, J.E., Rational mechanics, (1966), American Elsevier New York, § 5.4. · Zbl 0163.45902
[14] Kuhn, H.W.; Tucker, A.W., Nonlinear programming, () · Zbl 0044.05903
[15] Lemke, C.E.; Howson, J.T., Equilibrium points of bimatrix games, J. soc. indust. appl. math., 12, 413-423, (1964) · Zbl 0128.14804
[16] Lemke, C.E., Bimatrix equilibrium points and mathematical programming, Management sci., 11, 681-689, (1965) · Zbl 0139.13103
[17] C.E. Lemke, Private communication.
[18] Motzkin, T.S., Copositive quadratic forms, Nat. bur. standards report, 1818, 11-12, (1952)
[19] Nash, J.F., Noncooperative games, Ann. math., 54, 286-295, (1951) · Zbl 0045.08202
[20] Neumann, J.von, Discussion of a maximum problem, ()
[21] Panne, C.van de; Whinston, A., A composition of two methods for quadratic programming, Operations res., 14, 422-441, (1966) · Zbl 0138.41305
[22] Parson, T.D., A combinatorial approach to convex quadratic programming, ()
[23] Tucker, A.W., A combinatorial equivalence of matrices, () · Zbl 0096.00701
[24] Tucker, A.W., Principal pivotal transforms of square matrices, SIAM review, 5, 305, (1963)
[25] Tucker, A.W., Pivotal algebra, () · Zbl 0334.90033
[26] Wolfe, P., The simplex method for quadratic programming, Econometrica, 27, 1959, (1959)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.