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A Short Derivation of the Kuhn-Tucker Conditions

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DOI: 10.4236/ojop.2015.42006    4,545 Downloads   5,070 Views   Citations

ABSTRACT

The Kuhn-Tucker conditions have been used to derive many significant results in economics. However, thus far, their derivation has been a little bit troublesome. The author directly derives the Kuhn-Tucker conditions by applying a corollary of Farkas’s lemma under the Mangasarian-Fromovitz constraint qualification and shows the boundedness of Lagrange multipliers.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Tanaka, Y. (2015) A Short Derivation of the Kuhn-Tucker Conditions. Open Journal of Optimization, 4, 47-50. doi: 10.4236/ojop.2015.42006.

References

[1] Negishi, T. (1960) Welfare Economics and Existence of an Equilibrium for a Competitive Economy. Metroeconomica, 12, 92-97.
http://dx.doi.org/10.1111/j.1467-999X.1960.tb00275.x
[2] Rogerson, W.P. (1985) The First-Order Approach to Principal-Agent Problems. Econometrica, 53, 1357-1367.
http://dx.doi.org/10.2307/1913212
[3] Grossman, H.I. (1994) Production, Appropriation, and Land Reform. American Economic Review, 84, 705-712.
[4] Mas-Colell, A., Whinston, M.D. and Green, J.R. (1995) Microeconomic Theory. Oxford University Press, New York.
[5] Mangasarian, O.L. and Fromovitz, S. (1967) The Fritz John Necessary Optimality Conditions in the Presence of Equality and Inequality Constraints. Journal of Mathematical Analysis and Applications, 17, 37-47.
http://dx.doi.org/10.1016/0022-247X(67)90163-1
[6] Nocedal, J. and Wright, S.J. (2006) Numerical Optimization. 2nd Edition, Springer, Berlin.
[7] Bazaraa, M.S. and Shetty, C.M. (1979) Nonlinear Programming: Theory and Algorithms. 2nd Edition, Wiley, New York.
[8] Mangasarian, O.L. (1994) Nonlinear Programming. SIAM, Philadelphia.
http://dx.doi.org/10.1137/1.9781611971255

  
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