Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

A duality theorem for non-linear programming


Author: Philip Wolfe
Journal: Quart. Appl. Math. 19 (1961), 239-244
MSC: Primary 90.58
DOI: https://doi.org/10.1090/qam/135625
MathSciNet review: 135625
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Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] Jack B. Dennis, Mathematical programming and electrical networks, Technology Press, Cambridge' Mass., 1959 MR 0108400
  • [2] William S. Dorn, Duality in quadratic programming, Quart. Appl. Math. 18, No. 2, 155-162 (July 1960) MR 0112751
  • [3] William S. Dorn, A duality theorem for convex programs, IBM J. Research and Development 4, No. 4, 407-413 (Oct. 1960) MR 0114672
  • [4] A. J. Goldman and A. W. Tucker, Theory of linear programming, Linear Inequalities and Related Systems (Annals of Mathematics Study, No. 38), H. W. Kuhn and A. W. Tucker (eds.), Princeton University Press, 1956, pp. 53-97 MR 0101826
  • [5] James E. Kelley, Jr., The cutting-plane method for solving convex programs, J. Soc. Ind. and Appl. Math. 8, No. 4, 703-712 (Dec. 1960) MR 0118538
  • [6] H. W. Kuhn and A. W. Tucker, Nonlinear programming, Proc. 2nd Berkeley Symp. on Mathematical Statistics and Probability, University Of California Press, 1951, pp. 481-492 MR 0047303
  • [7] Philip Wolfe, The simplex method for quadratic programming, Econometrica 27, No. 3, 382-398 (July 1959) MR 0106783

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DOI: https://doi.org/10.1090/qam/135625
Article copyright: © Copyright 1961 American Mathematical Society

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