Fritz John Duality in the Presence of Equality and Inequality Constraints | Zendy

Iqbal Husain | Zendy; Santosh Kumar Shrivastav | Zendy

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Fritz John Duality in the Presence of Equality and Inequality Constraints

Author(s) -

Iqbal Husain,

Santosh Kumar Shrivastav

Publication year - 2012

Publication title -

applied mathematics

Language(s) - English

Resource type - Journals

eISSN - 2152-7393

pISSN - 2152-7385

DOI - 10.4236/am.2012.39151

Subject(s) - converse , duality (order theory) , wolfe duality , convexity , strong duality , mathematics , duality gap , weak duality , dual (grammatical number) , constraint (computer aided design) , mathematical economics , inequality , mathematical optimization , pure mathematics , optimization problem , mathematical analysis , philosophy , economics , finance , linguistics , geometry

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

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