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On symmetric gH-derivative: Applications to dual interval-valued optimization problems

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  • Guo, Yating
  • Ye, Guoju
  • Liu, Wei
  • Zhao, Dafang
  • Treanţă, Savin

Abstract

This paper provides a complete study on properties of symmetric gH-derivative. More precisely, a necessary and sufficient condition for the symmetric gH-differentiability of interval-valued functions is presented. Further, we clarify the relationship between the symmetric gH-differentiability and gH-differentiability. Moreover, quasi-mean value theorem, chain rule and some operations of symmetric gH-differentiable interval-valued functions are established. As applications, we develop the Mond–Weir duality theory for a class of symmetric gH-differentiable interval-valued optimization problems. Weak, strong and strict converse duality theorems are formulated and proved. Also, several examples are presented in order to support the corresponding theoretical results.

Suggested Citation

  • Guo, Yating & Ye, Guoju & Liu, Wei & Zhao, Dafang & Treanţă, Savin, 2022. "On symmetric gH-derivative: Applications to dual interval-valued optimization problems," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922002788
    DOI: 10.1016/j.chaos.2022.112068
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    References listed on IDEAS

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    Cited by:

    1. Guo, Yating & Ye, Guoju & Liu, Wei & Zhao, Dafang & Treanţǎ, Savin, 2023. "Solving nonsmooth interval optimization problems based on interval-valued symmetric invexity," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Zhang, Chuang-liang & Huang, Nan-jing & O’Regan, Donal, 2023. "On variational methods for interval-valued functions with some applications," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    3. Savin Treanţă & Tareq Saeed, 2023. "On Weak Variational Control Inequalities via Interval Analysis," Mathematics, MDPI, vol. 11(9), pages 1-11, May.

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