Fritz John Duality in the Presence of Equality and Inequality Constraints

Affiliation(s)

Department of Mathematics, Jaypee University of Engineering and Technology, Guna, India.

Department of Mathematics, Jaypee University of Engineering and Technology, Guna, India.

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.

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.

I. Husain and S. Shrivastav, "Fritz John Duality in the Presence of Equality and Inequality Constraints,"

References

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