Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Duality theorems and theorems of the alternative


Author: L. McLinden
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 41 #3098. MR 0258451 (41:3098)
  • [2] O. L. Mangasarian, Nonlinear programming, McGraw-Hill, New York, 1969. MR 40 #5263. MR 0252038 (40:5263)
  • [3] L. McLinden, Transposition theorems, old and new (in preparation).
  • [4] R. T. Rockafellar, Convex analysis, Princeton Math. Ser., no. 28, Princeton Univ. Press, Princeton, N. J., 1970. MR 43 #445. MR 0274683 (43:445)
  • [5] -, Conjugate duality and optimization, CBMS Regional Conf. Ser., no. 16, SIAM, Philadelphia, Pa., 1975.
  • [6] J. Stoer and C. Witzgall, Convexity and optimization in finite dimensions. I, Die Grundlehren der math. Wissenschaften, Band 163, Springer-Verlag, Berlin and New York, 1970. MR 44 #3707. MR 0286498 (44:3707)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 90C30, 49B40

Retrieve articles in all journals with MSC: 90C30, 49B40


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0395848-1
Keywords: Transposition theorems, dual extremum problems
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society