A duality theorem for non-linear programming
Author:
Philip Wolfe
Journal:
Quart. Appl. Math. 19 (1961), 239-244
MSC:
Primary 90.58
DOI:
https://doi.org/10.1090/qam/135625
MathSciNet review:
135625
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Abstract: A dual problem is formulated for the mathematical programming problem of minimizing a convex function under convex constraints which reduces to the classical dual problem in the case of linear programming problems. Duality theorems are proved regarding the relationship between the problem and its dual.
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Jack B. Dennis, Mathematical programming and electrical networks, Technology Press, Cambridge’ Mass., 1959
William S. Dorn, Duality in quadratic programming, Quart. Appl. Math. 18, No. 2, 155–162 (July 1960)
William S. Dorn, A duality theorem for convex programs, IBM J. Research and Development 4, No. 4, 407–413 (Oct. 1960)
A. J. Goldman and A. W. Tucker, Theory of linear programming, Linear Inequalities and Related Systems (Annals of Mathematics Study, No. 38), H. W. Kuhn and A. W. Tucker (eds.), Princeton University Press, 1956, pp. 53–97
James E. Kelley, Jr., The cutting-plane method for solving convex programs, J. Soc. Ind. and Appl. Math. 8, No. 4, 703–712 (Dec. 1960)
H. W. Kuhn and A. W. Tucker, Nonlinear programming, Proc. 2nd Berkeley Symp. on Mathematical Statistics and Probability, University Of California Press, 1951, pp. 481–492
Philip Wolfe, The simplex method for quadratic programming, Econometrica 27, No. 3, 382–398 (July 1959)
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Article copyright:
© Copyright 1961
American Mathematical Society
