DOI: 10.1090/qam/135625. A duality theorem for non-linear programming

A duality theorem for non-linear programming

10.1090/qam/135625

Crossref journal-article

American Mathematical Society (AMS)

Quarterly of Applied Mathematics (14)

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.

Bibliography

Wolfe, P. (1961). A duality theorem for non-linear programming. Quarterly of Applied Mathematics, 19(3), 239â244.

Authors 1

Philip Wolfe (first)

References 7 Referenced 489

{'volume-title': 'Mathematical programming and electrical networks', 'year': '1959', 'author': 'Dennis, Jack B.', 'key': '1'} / Mathematical programming and electrical networks by Dennis, Jack B. (1959)
10.1090/qam/112751 / Quart. Appl. Math. / Duality in quadratic programming by Dorn, W. S. (1960)
10.1147/rd.44.0407 / IBM J. Res. Develop. / A duality theorem for convex programs by Dorn, W. S. (1960)
{'key': '4', 'first-page': '53', 'article-title': 'Theory of linear programming', 'author': 'Goldman, A. J.', 'year': '1956'} / Theory of linear programming by Goldman, A. J. (1956)
10.1137/0108053 / J. Soc. Indust. Appl. Math. / The cutting-plane method for solving convex programs by Kelley, J. E., Jr. (1960)
{'key': '6', 'first-page': '481', 'article-title': 'Nonlinear programming', 'author': 'Kuhn, H. W.', 'year': '1951'} / Nonlinear programming by Kuhn, H. W. (1951)
10.2307/1909468 / Econometrica / The simplex method for quadratic programming by Wolfe, Philip (1959)

Dates

Type	When
Created	8 years, 8 months ago (Dec. 14, 2016, 6:28 p.m.)
Deposited	10 months, 1 week ago (Oct. 25, 2024, noon)
Indexed	1 week, 2 days ago (Aug. 27, 2025, 12:35 p.m.)
Issued	63 years, 11 months ago (Oct. 1, 1961)
Published	63 years, 11 months ago (Oct. 1, 1961)
Published Print	63 years, 11 months ago (Oct. 1, 1961)

Funders 0

None

BibTeX

@article{Wolfe_1961, title={A duality theorem for non-linear programming}, volume={19}, ISSN={1552-4485}, url={http://dx.doi.org/10.1090/qam/135625}, DOI={10.1090/qam/135625}, number={3}, journal={Quarterly of Applied Mathematics}, publisher={American Mathematical Society (AMS)}, author={Wolfe, Philip}, year={1961}, month=oct, pages={239–244} }

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