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

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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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Authors and Affiliations

  1. Department of Applied Mathematics, Chung-Yuan Christian University, Chung Li, 320, Taiwan

    H. C. Lai & T. Y. Huang

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  1. H. C. Lai
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  2. T. Y. Huang
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Correspondence to H. C. Lai.

Additional information

Communicated by P.L. Yu.

This research was partly supported by the National Science Council, NSC 94-2115-M-033-003, Taiwan.

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Lai, H.C., Huang, T.Y. Minimax Fractional Programming for n-Set Functions and Mixed-Type Duality under Generalized Invexity. J Optim Theory Appl 139, 295–313 (2008). https://doi.org/10.1007/s10957-008-9410-6

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