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Some Results on $$\sigma $$ σ -Convex Functions and Fréchet $$\sigma $$ σ -Subdifferentials

Author

Listed:
  • Mohammad Hossein Alizadeh

    (Institute for Advanced Studies in Basic Sciences (IASBS))

  • Nasim Nazari

    (Institute for Advanced Studies in Basic Sciences (IASBS))

  • Alireza Youhannaee Zanjani

    (Institute for Advanced Studies in Basic Sciences (IASBS))

Abstract

We study the directional derivative of the $$\sigma $$ σ -convex function and investigate its mutual relation with $$\sigma $$ σ -subdifferential. Additionally, we introduce the notion of limiting Fréchet $$\sigma $$ σ -subdifferential and then present some results regarding the Fréchet $$\sigma $$ σ -subdifferential, limiting Fréchet $$\sigma $$ σ -subdifferential and $$\sigma $$ σ -Fréchet normals.

Suggested Citation

  • Mohammad Hossein Alizadeh & Nasim Nazari & Alireza Youhannaee Zanjani, 2025. "Some Results on $$\sigma $$ σ -Convex Functions and Fréchet $$\sigma $$ σ -Subdifferentials," Journal of Optimization Theory and Applications, Springer, vol. 207(3), pages 1-27, December.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:3:d:10.1007_s10957-025-02808-z
    DOI: 10.1007/s10957-025-02808-z
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    References listed on IDEAS

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    1. Felipe Lara & Alireza Kabgani, 2021. "On global subdifferentials with applications in nonsmooth optimization," Journal of Global Optimization, Springer, vol. 81(4), pages 881-900, December.
    2. A. Kabgani & F. Lara, 2022. "Strong subdifferentials: theory and applications in nonconvex optimization," Journal of Global Optimization, Springer, vol. 84(2), pages 349-368, October.
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