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 | References | Similar Articles | Additional Information

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.

**[1]**J. B. Dennis,*Mathematical programming and electrical networks*, Wiley, New York, N. Y., 1959 MR**0108400****[2]**W. S. Dorn,*Duality in quadratic programming*, Q. Appl. Math.,**18**, 155-162 (1960) MR**0112751****[3]**W. S. Dorn,*A duality theorem for convex programs*, IBM J. Res. Dev.,**4**, 407-413 (1960) MR**0114672****[4]**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. MR**0046018****[5]**M. A. Hanson,*A duality theorem in nonlinear programming with nonlinear constraints*, Austral. J. Statist.,**3**, 64-72 (1961) MR**0138508****[6]**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 MR**0047303****[7]**P. Wolfe,*A duality theorem for nonlinear programming*, Q. Appl. Math.,**19**, 239-244 (1961) MR**0135625****[8]**P. Huard,*Dual programs*, IBM J. Res. Dev.,**6**, 137-139 (1962) MR**0156708**

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DOI:
https://doi.org/10.1090/qam/141530

Article copyright:
© Copyright 1962
American Mathematical Society