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Generalizations of Higher-Order Duality for Multiple Objective Nonlinear Programming under the Generalizations of Type-I Functions

Author

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  • Mohamed Abd El-Hady Kassem

    (Department of Mathematics, Faculty of Science, Tanta University, Tanta 31111, Egypt)

  • Huda M. Alshanbari

    (Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

Abstract

In this study, we introduce new generalizations of higher-order type-I functions and higher-order pseudo-convexity type-I functions. The application of the notion of sublinear functionals to these generalizations of higher-order type-I and higher-order pseudo-convexity type-I functions is crucial to our main findings. Furthermore, under these generalizations of the higher-order type-I and higher-order pseudo-convexity type-I functions, we established and studied six new types of higher-order duality models and programs for multiple objective nonlinear programming problems. In addition, we use these generalizations of higher-order type-I functions and higher-order pseudo-convexity type-I functions, to formulate and prove the theorems of weak duality, strong duality, and strict converse duality for these new six types of higher-order model programs.

Suggested Citation

  • Mohamed Abd El-Hady Kassem & Huda M. Alshanbari, 2023. "Generalizations of Higher-Order Duality for Multiple Objective Nonlinear Programming under the Generalizations of Type-I Functions," Mathematics, MDPI, vol. 11(4), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:889-:d:1063564
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    References listed on IDEAS

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    1. Shashi Kant Mishra & Shouyang Wang & Kin Keung Lai, 2008. "V-Invex Functions and Vector Optimization," Springer Optimization and Its Applications, Springer, number 978-0-387-75446-8, December.
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    Cited by:

    1. Adrian Marius Deaconu & Daniel Tudor Cotfas & Petru Adrian Cotfas, 2023. "Advanced Optimization Methods and Applications," Mathematics, MDPI, vol. 11(9), pages 1-7, May.

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