Duality theorems and theorems of the alternative
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- by L. McLinden PDF
- Proc. Amer. Math. Soc. 53 (1975), 172-175 Request permission
Abstract:
It is shown, in a completely general setting, that a theorem of the alternative is logically equivalent to a duality theorem linking two constrained optimization problems.References
- M. L. Balinski and A. W. Tucker, Duality theory of linear programs: A constructive approach with applications, SIAM Rev. 11 (1969), 347–377. MR 258451, DOI 10.1137/1011060
- Olvi L. Mangasarian, Nonlinear programming, McGraw-Hill Book Co., New York-London-Sydney, 1969. MR 0252038 L. McLinden, Transposition theorems, old and new (in preparation).
- R. Tyrrell Rockafellar, Convex analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, N.J., 1970. MR 0274683 —, Conjugate duality and optimization, CBMS Regional Conf. Ser., no. 16, SIAM, Philadelphia, Pa., 1975.
- Josef Stoer and Christoph Witzgall, Convexity and optimization in finite dimensions. I, Die Grundlehren der mathematischen Wissenschaften, Band 163, Springer-Verlag, New York-Berlin, 1970. MR 0286498
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 53 (1975), 172-175
- MSC: Primary 90C30; Secondary 49B40
- DOI: https://doi.org/10.1090/S0002-9939-1975-0395848-1
- MathSciNet review: 0395848