Duality in nonlinear programming
Author:
O. L. Mangasarian
Journal:
Quart. Appl. Math. 20 (1962), 300-302
MSC:
Primary 90.58
DOI:
https://doi.org/10.1090/qam/141530
Correction:
Quart. Appl. Math. 21 (1963), 252-252.
MathSciNet review:
141530
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Abstract: The main result of this work is a converse theorem to a duality theorem for nonlinear programming recently established by Wolfe. The conditions on the present theorem are slightly stronger than those imposed by Wolfe. Hanson has given a different proof of a similar theorem but without stating in the theorem some important assumptions made in the proof.†
- Jack B. Dennis, Mathematical programming and electrical networks, Technology Press of The Massachusetts Institute of Technology, Cambridge, Mass.; John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1959. MR 0108400
- W. S. Dorn, Duality in quadratic programming, Quart. Appl. Math. 18 (1960/61), 155–162. MR 112751, DOI 10.1090/S0033-569X-1960-0112751-2
- W. S. Dorn, A duality theorem for convex programs, IBM J. Res. Develop. 4 (1960), 407–413. MR 114672, DOI 10.1147/rd.44.0407
- David Gale, Harold W. Kuhn, and Albert W. Tucker, Linear programming and the theory of games, Activity Analysis of Production and Allocation, Cowles Commission Monograph No. 13, John Wiley & Sons, Inc., New York, N.Y.; Chapman & Hall, Ltd., London, 1951, pp. 317–329. MR 0046018
- M. A. Hanson, A duality theorem in non-linear programming with non-linear constraints, Austral. J. Statist. 3 (1961), 64–72. MR 138508, DOI 10.1111/j.1467-842X.1961.tb00310.x
- H. W. Kuhn and A. W. Tucker, Nonlinear programming, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley-Los Angeles, Calif., 1951, pp. 481–492. MR 0047303
- Philip Wolfe, A duality theorem for non-linear programming, Quart. Appl. Math. 19 (1961), 239–244. MR 135625, DOI 10.1090/S0033-569X-1961-0135625-6
- Pierre Huard, Dual programs, Recent advances in mathematical programming, McGraw-Hill, New York, 1963, pp. 55–62. MR 0156708
J. B. Dennis, Mathematical programming and electrical networks, Wiley, New York, N. Y., 1959
W. S. Dorn, Duality in quadratic programming, Q. Appl. Math., 18, 155-162 (1960)
W. S. Dorn, A duality theorem for convex programs, IBM J. Res. Dev., 4, 407-413 (1960)
D. Gale, H. W. Kuhn, A. W. Tucker, Linear programming and the theory of games, Chapter 19 of Activity Analysis of Production and Allocation, Wiley, New York, 1951.
M. A. Hanson, A duality theorem in nonlinear programming with nonlinear constraints, Austral. J. Statist., 3, 64-72 (1961)
H. W. Kuhn and A. W. Tucker, Nonlinear programming, Proceedings, 2nd Berkeley Symp. in math. statist. and probab., Univ. California Press, 1951, pp. 481-492
P. Wolfe, A duality theorem for nonlinear programming, Q. Appl. Math., 19, 239-244 (1961)
P. Huard, Dual programs, IBM J. Res. Dev., 6, 137-139 (1962)
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Article copyright:
© Copyright 1962
American Mathematical Society
