Minimax Fractional Programming for n-Set Functions and Mixed-Type Duality under Generalized Invexity

Minimax Fractional Programming for n-Set Functions and Mixed-Type Duality under Generalized Invexity

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Article ID: iaor200912335
Country: United States
Volume: 139
Issue: 2
Start Page Number: 295
End Page Number: 313
Publication Date: Nov 2008
Journal: Journal of Optimization Theory and Applications
Authors: ,
Keywords: duality, invexity, programming (minimax)
Abstract:

We establish the sufficient optimality conditions for a minimax programming problem involving p fractional n–set functions under generalized invexity. Using incomplete Lagrange duality, we formulate a mixed–type dual problem which unifies the Wolfe type dual and Mond–Weir type dual in fractional n–set functions under generalized invexity. Furthermore, we establish three duality theorems: weak, strong, and strict converse duality theorem, and prove that the optimal values of the primal problem and the mixed–type dual problem have no duality gap under extra assumptions in the framework.

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