AM  Vol.3 No.9 , September 2012
Fritz John Duality in the Presence of Equality and Inequality Constraints
ABSTRACT
A dual for a nonlinear programming problem in the presence of equality and inequality constraints which represent many realistic situation, is formulated which uses Fritz John optimality conditions instead of the Karush-Kuhn-Tucker optimality conditions and does not require a constraint qualification. Various duality results, namely, weak, strong, strict-converse and converse duality theorems are established under suitable generalized convexity. A generalized Fritz John type dual to the problem is also formulated and usual duality results are proved. In essence, the duality results do not require any regularity condition if the formulations of dual problems uses Fritz John optimality conditions.

Cite this paper
I. Husain and S. Shrivastav, "Fritz John Duality in the Presence of Equality and Inequality Constraints," Applied Mathematics, Vol. 3 No. 9, 2012, pp. 1023-1028. doi: 10.4236/am.2012.39151.
References
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[4]   O. L. Mangasarian and S. Fromovitz, “The Fritz John Necessary Optimality Conditions in the Presence of Equality and Inequality Constraints,” Journal of Mathematical Analysis and Applications, Vol. 17, No. 1, 1967, pp. 37-47. doi:10.1016/0022-247X(67)90163-1

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[6]   O. L. Mangasarian, “Nonlinear Programming,” McGrawHill, New York, 1969.

 
 
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