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

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Listed:
  • H. C. Lai

    (Chung-Yuan Christian University)

  • T. Y. Huang

    (Chung-Yuan Christian University)

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.

Suggested Citation

  • H. C. Lai & T. Y. Huang, 2008. "Minimax Fractional Programming for n-Set Functions and Mixed-Type Duality under Generalized Invexity," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 295-313, November.
    • Handle: RePEc:spr:joptap:v:139:y:2008:i:2:d:10.1007_s10957-008-9410-6
    DOI: 10.1007/s10957-008-9410-6
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    References listed on IDEAS

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    1. H. C. Lai & J. C. Liu & K. Tanaka, 1999. "Duality Without a Constraint Qualification for Minimax Fractional Programming," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 109-125, April.
    2. Jin-Chirng Lee & Hang-Chin Lai, 2005. "Parameter-Free Dual Models for Fractional Programming with Generalized Invexity," Annals of Operations Research, Springer, vol. 133(1), pages 47-61, January.
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