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

H. C. Lai () and T. Y. Huang
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H. C. Lai: Chung-Yuan Christian University
T. Y. Huang: Chung-Yuan Christian University

Journal of Optimization Theory and Applications, 2008, vol. 139, issue 2, No 6, 295-313

Abstract: 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.

Keywords: Minimax fractional programming; Partial differentiable n-set function; Mixed-type dual; Duality theorems; Quasi/Pseudo-invex set function (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10957-008-9410-6

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