Duality in quadratic programming
Author:
W. S. Dorn
Journal:
Quart. Appl. Math. 18 (1960), 155-162
MSC:
Primary 90.00
DOI:
https://doi.org/10.1090/qam/112751
MathSciNet review:
112751
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Abstract: A proof, based on the duality theorem of linear programming, is given for a duality theorem for a class of quadratic programs. An illustrative application is made in the theory of elastic structures.
- E. M. L. Beale, On minimizing a convex function subject to linear inequalities, J. Roy. Statist. Soc. Ser. B 17 (1955), 173–184; discussion, 194–203. (Symposium on linear programming). MR 89101
A. Charnes and C. E. Lemke, The continuous limit method I; minimization of convex functionals over convex polyhedra; presented at Am. Math. Soc. Meeting, Cambridge, Mass., Aug. 1958
- Marguerite Frank and Philip Wolfe, An algorithm for quadratic programming, Naval Res. Logist. Quart. 3 (1956), 95–110. MR 89102, DOI https://doi.org/10.1002/nav.3800030109
- Clifford Hildreth, A quadratic programming procedure, Naval Res. Logist. Quart. 4 (1957), 79–85. MR 89100, DOI https://doi.org/10.1002/nav.3800040113
Philip Wolfe, The simplex method for quadratic programming, RAND Rep. P-1205, Oct. 1957
Jack B. Dennis, A dual problem for a class of quadratic programs, MIT Research Note No. 1, Nov. 1957
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- 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
G. B. Dantzig and A. Orden, A duality theorem based on the simplex method, Symposium on Linear Inequalities and Programming, Project SCOOP, 51-55, 1951
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
J. Nielsen, Vorlesungen über elementare Mechanik, Julius Springer, Berlin, 1935
E. M. L. Beale, On minimizing a convex function subject to linear inequalities, J. Roy. Statistical Soc. (Ser. B) 17, 173-177 (1955)
A. Charnes and C. E. Lemke, The continuous limit method I; minimization of convex functionals over convex polyhedra; presented at Am. Math. Soc. Meeting, Cambridge, Mass., Aug. 1958
M. Frank and P. Wolfe, An algorithm for quadratic programming, Naval Research Log. Quart. 3, 95-110 (March-June 1956)
C. Hildreth, A quadratic programming procedure, Naval Research Log. Quart. 4, 79-85 (March 1957)
Philip Wolfe, The simplex method for quadratic programming, RAND Rep. P-1205, Oct. 1957
Jack B. Dennis, A dual problem for a class of quadratic programs, MIT Research Note No. 1, Nov. 1957
H. W. Kuhn and A. W. Tucker, Nonlinear programming, Proc. 2nd Berkeley Symposium on Math. Statistics and Probability, 481-492, 1951
D. Gale, H. W. Kuhn and A. W. Tucker, Linear programming and the theory of games, Chap. XIX of Activity analysis of products and allocation, Cowles Commission Monograph 13, John Wiley and Sons, New York, 1951
G. B. Dantzig and A. Orden, A duality theorem based on the simplex method, Symposium on Linear Inequalities and Programming, Project SCOOP, 51-55, 1951
R. Courant and D. Hilbert, Methods of mathematical physics, Interscience, New York, 1953
J. Nielsen, Vorlesungen über elementare Mechanik, Julius Springer, Berlin, 1935
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Article copyright:
© Copyright 1960
American Mathematical Society
