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The Sufficiency of Solutions for Non-smooth Minimax Fractional Semi-Infinite Programming with ( B K ,ρ )−Invexity

Author

Listed:
  • Hong Yang

    (School of Mathematics and Statistics, Yulin University, Yulin 719000, China)

  • Angang Cui

    (School of Mathematics and Statistics, Yulin University, Yulin 719000, China)

Abstract

Minimax fractional semi-infinite programming is an important research direction for semi-infinite programming, and has a wide range of applications, such as military allocation problems, economic theory, cooperative games, and other fields. Convexity theory plays a key role in many aspects of mathematical programming and is the foundation of mathematical programming research. The relevant theories of semi-infinite programming based on different types of convex functions have their own applicable scope and limitations. It is of great value to study semi-infinite programming on the basis of more generalized convex functions and obtain more general results. In this paper, we defined a new type of generalized convex function, based on the concept of the K −directional derivative, that is, uniform ( B K , ρ ) − invex, strictly uniform ( B K , ρ ) − invex, uniform ( B K , ρ ) − pseudoinvex, strictly uniform ( B K , ρ ) − pseudoinvex, uniform ( B K , ρ ) − quasiinvex and weakly uniform ( B K , ρ ) − quasiinvex function. Then, we studied a class of non-smooth minimax fractional semi-infinite programming problems involving this generalized convexity and obtained sufficient optimality conditions.

Suggested Citation

  • Hong Yang & Angang Cui, 2023. "The Sufficiency of Solutions for Non-smooth Minimax Fractional Semi-Infinite Programming with ( B K ,ρ )−Invexity," Mathematics, MDPI, vol. 11(20), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4240-:d:1257146
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    References listed on IDEAS

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    1. Jean-Philippe Vial, 1983. "Strong and Weak Convexity of Sets and Functions," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 231-259, May.
    2. VIAL, Jean-Philippe, 1983. "Strong and weak convexity of sets and functions," LIDAM Reprints CORE 529, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. J. J. Rückmann & A. Shapiro, 1999. "First-Order Optimality Conditions in Generalized Semi-Infinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 677-691, June.
    4. D. H. Yuan & X. L. Liu & A. Chinchuluun & P. M. Pardalos, 2006. "Nondifferentiable Minimax Fractional Programming Problems with (C, α, ρ, d)-Convexity," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 185-199, April.
    5. Z. A. Liang & H. X. Huang & P. M. Pardalos, 2001. "Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 611-619, September.
    6. Francisco Guerra-Vázquez & Jan-J. Rückmann & Ralf Werner, 2012. "On saddle points in nonconvex semi-infinite programming," Journal of Global Optimization, Springer, vol. 54(3), pages 433-447, November.
    7. M. H. Kim & G. M. Lee, 2001. "On Duality Theorems for Nonsmooth Lipschitz Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 110(3), pages 669-675, September.
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