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Complex Minimax Fractional Programming of Analytic Functions

Author

Listed:
  • H. C. Lai

    (Chung-Yuan Christian University)

  • J. C. Liu

    (National Taiwan Normal University)

  • S. Schaible

    (University of California)

Abstract

We prove that a minmax fractional programming problem is equivalent to a minimax nonfractional parametric problem for a given parameter in complex space. Using a parametric approach, we establish the Kuhn-Tucker type necessary optimality conditions and prove the existence theorem of optimality for complex minimax fractional programming in the framework of generalized convexity. Subsequently, we apply the optimality conditions to formulate a one-parameter dual problem and prove weak duality, strong duality, and strict converse duality theorems involving generalized convex complex functions.

Suggested Citation

  • H. C. Lai & J. C. Liu & S. Schaible, 2008. "Complex Minimax Fractional Programming of Analytic Functions," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 171-184, April.
    • Handle: RePEc:spr:joptap:v:137:y:2008:i:1:d:10.1007_s10957-007-9332-8
    DOI: 10.1007/s10957-007-9332-8
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    References listed on IDEAS

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    1. J. C. Chen & H. C. Lai & S. Schaible, 2005. "Complex Fractional Programming and the Charnes-Cooper Transformation," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 203-213, July.
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    Cited by:

    1. Tone-Yau Huang, 2020. "Second-Order Parametric Free Dualities for Complex Minimax Fractional Programming," Mathematics, MDPI, vol. 8(1), pages 1-12, January.
    2. Jiawei Chen & Suliman Al-Homidan & Qamrul Hasan Ansari & Jun Li & Yibing Lv, 2021. "Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 221-243, April.
    3. Hang-Chin Lai & Tone-Yau Huang, 2012. "Nondifferentiable minimax fractional programming in complex spaces with parametric duality," Journal of Global Optimization, Springer, vol. 53(2), pages 243-254, June.

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