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Proceedings of the American Mathematical Society

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Duality theorems and theorems of the alternative

Author: L. McLinden
Journal: Proc. Amer. Math. Soc. 53 (1975), 172-175
MSC: Primary 90C30; Secondary 49B40
MathSciNet review: 0395848
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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 [Enhancements On Off] (What's this?)

  • [1] M. L. Balinski and A. W. Tucker, Duality theory of linear programs: A constructive approach with applications, SIAM Rev. 11 (1969), 347–377. MR 0258451
  • [2] Olvi L. Mangasarian, Nonlinear programming, McGraw-Hill Book Co., New York-London-Sydney, 1969. MR 0252038
  • [3] L. McLinden, Transposition theorems, old and new (in preparation).
  • [4] R. Tyrrell Rockafellar, Convex analysis, Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, N.J., 1970. MR 0274683
  • [5] -, Conjugate duality and optimization, CBMS Regional Conf. Ser., no. 16, SIAM, Philadelphia, Pa., 1975.
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Keywords: Transposition theorems, dual extremum problems
Article copyright: © Copyright 1975 American Mathematical Society